This  book  is  DUE  on  the  last  date  stamped  below 


JAN  4      1926 


i 


CO  CO 


C_)  CO  CD 


NATURAL     PHILOSOPHY 


FOR   THE    USE   OF 


ana  ScaUemies, 


BY 

J.   A.   GILLET, 

PROFESSOR  OF   PHYSICS   IN   THE   NORMAL  COLLEGB  OF  THE  CITY  OF  NEW  YORK, 


W.  J.   ROLFE, 

FORMERLY  HEAD  MASTER  OF  THB   HIGH  SCHOOL, 
CAMBRIDGE,    MASS. 


POTTER,    AINSWORTH,    &    CO. 

NEW   YORK   AND   CHICAGO. 

188.1, 


56202 


Copyright,  1881, 
BY  J.   A.   GlLLET  AND    W.   J.    ROLFE. 


Franklin  Press:    Rand,  Avery,  &=  Co.,  Bosto 


-I 


PREFACE. 


IT  has  been  the  aim  of  the  authors  to  state  in  clear, 
simple,  and  accurate  terms  the  elementary  facts  and  prin- 
ciples of  Physics  as  they  are  understood  at  the  present 
time,  and  the  most  important  practical  applications  of 
these  principles.  This  book  is  in  no  sense  a  revision 
of  the  Natural  Philosophy  of  the  "  Cambridge  Course  of 
Physics,"  but  an  entirely  new  and  independent  work, 
differing  from  the  earlier  work  both  in  matter  and  in 
method  of  presentation. 

The  authors  have  striven  to  give  due  prominence  to 
every  department  of  the  subject,  and  at  the  same  time 
to  bring  the  whole  within  reasonable  limits.  The  province 
of  Physics  is  now  so  extensive,  while  the  time  allotted  to 
its  study  in  our  schools  is  usually  so  brief,  and  the  tastes 
of  teachers  and  the  capacities  of  classes  are  so  varied,  that 
it  is  impossible  to  prepare  a  text-book  that  shall  meet  the 
requirements  of  all.  The  authors  have  endeavored  to 
adapt  this  book  to  the  wants  of  the  greatest  possible 
number  by  the  use  of  two  kinds  of  type.  The  funda- 
mental facts  and  principles,  and  the  simplest  applications 
of  these  principles,  are  printed  in  the  coarser  type.  It  is 


hoped  that  these  portions  will  furnish  a  course  in  Physics 
brief  enough  for  those  whose  time  is  most  limited.  The 
matter  in  the  finer  type  may  make  the  book  acceptable  to 
many  teachers  who  have  more  than  enough  time  at  their 
disposal  for  the  briefer  course,  as  it  will  enable  them  to 
pursue  any  subject  at  greater  length,  according  to  their 
individual  tastes,  the  ability  of  their  classes,  or  the  appara- 
tus at  their  disposal.  The  teacher  may  also  be  able  to 
meet  the  different  tastes  and  capacities  of  the  same  class, 
by  requiring  those  who  are  slow  of  apprehension  and  have 
little  aptitude  for  Physics  to  master  only  the  portion  in 
coarse  print ;  and  inducing  others,  who  are  interested  in 
the  subject  and  able  to  cope  with  it,  to  study  portions  of 
the  fine  print  also.  It  will  be  found  that  both  kinds 
of  type  are  very  clear  and  legible. 

The  matter  in  coarse  type  is  entirely  independent  of 
that  in  the  fine  type,  but  there  is  no  violent  dislocation 
between  the  two.  The  manuscript  was  first  prepared 
without  any  reference  to  the  parts  which  were  to  appear 
in  different  type,  and  the  sections  and  paragraphs  for 
the  coarse  type  were  selected  afterwards.  After  the 
selection  for  coarse  type  had  been  made,  only  very  slight 
alterations  were  found  to  be  necessary  to  render  these 
portions  independent  of  the  others. 

It  would  be  impossible  to  give  all  the  sources  from 
which  the  material  of  the  text  has  been  derived,  since  very 
much  of  it  is  presented  in  the  form  in  which  it  has  shaped 
itself  in  the  mind  of  one  of  the  authors  during  many  years 
of  daily  oral  teaching.  Considerable  material  has,  how- 
ever, been  drawn  from  Deschanel's  Natural  Philosophy, 
Gordon's  Electricity,  Loomis's  Meteorology,  and  other 


PREFACE.  V 

standard  works.  Theories  have  been  given,  as  a  rule, 
either  in  the 'words  of  their  authors  or  of  some  recognized 
authority ;  and  many  facts  and  illustrations  have  been 
taken  from  the  above-named  and  similar  works  with  little 
or  no  alteration  of  expression. 

The  majority  of  the  diagrams  in  Light  and  Electricity 
are  from  original  drawings.  All  the  other  cuts  have  been 
copied  and  reduced  in  size  by  the  phototype  process  from 
standard  works.  The  majority  of  the  cuts  have  been 
taken  from  Deschanel's  Philosophy,  Gordon's  Electricity, 
and  Loomis's  Meteorology.  The  following  list  contains 
about  all  the  books  from  which  material  of  any  kind  has 
been  drawn.  These  books  are  all  invaluable  to  teachers 
and  others  interested  in  Physics. 

Deschanel's   Natural  Philosophy.      D.  Appleton  &  Co. :   New 

York  (reprint). 

Ganot's  Physics.     Wm.  Wood  &  Co.  :   New  York  (reprint). 
Tail's    Recent  Advances  in  Physical  Science.      Macmillan  & 

Co. :   New  York. 

Maxwell's  Matter  and  Motion.     Macmillan  &  Co.  :  New  York. 
Tyndall's  Sound.     D.  Appleton  &  Co.  :    New  York  (reprint). 
Mayer's  Sound.     D.  Appleton  &  Co.  :  New  York. 
Helmholtz's    Popular    Lectures      1st  Series.     D.   Appleton  & 

Co.  :   New  York  (reprint). 

Taylor's  Sound  and  Music.    Macmillan  &  Co.  :  New  York. 
Tyndall's  Heat  a  Mode  of  Motion.     D.  Appleton  &  Co.  :  New 

York  (reprint). 
Maxwell's   Theory  of  Heat.     D.  Appleton  &  Co. :  New  York 

(reprint). 

Mayer's  Light.     D.  Appleton  &  Co.  :   New  York. 
Tyndall's  Lectures  on  Light.     D.  App'eton  &  Co. :  New  York. 
Rood's  Modern  Chromatics.     D.  Appleton  &  Co.  :   New  York. 
Jeffries's  Color  Blindness.     Houghton,  Mifflin,  &  Co.  :  Boston. 
Gordon's    Electricity    and    Magnetism.     D.   Appleton  &   Co.  : 

New  York  (reprint). 


VI  PREFACE. 

Jenkin's    Electricity   and    Magnetism.      D.    Appleton   &  Co.  : 

New  York  (reprint). 
Tyndall's  Lessons  in  Electricity.     D.  Appleton  &  Co.  :   New 

York  (reprint). 

Prescott's  Telegraph.     D.  Appleton  &  Co.  :   New  York. 
Prescott's  Telephone,  etc.     D.  Appleton  &  Co. :  New  York. 
Sawyer's  Electric  Lighting.     D.  Van  Nostrand  :  New  York. 
Loomis's  Meteorology.     Harper  &  Brothers  :   New  York. 
Stewart's  Energy.     D.  Appleton  &  Co.  :   New  York. 


CONTENTS. 


PAGE 

I.  CONSTITUTION    OF   MATTER 3 

II.  MECHANICS 9 

A.  DEFINITIONS.  —  UNITS.  —  NEWTON'S  LAWS  OF  MO- 

TION      9 

B.  WORK  AND  ENERGY 23 

C.  COMPOSITION  AND  RESOLUTION  OF  FORCES      ...  29 

D.  GRAVITY  AND  EQUILIBRIUM 34 

E.  FALLING  BODIES 42 

F.  THE  PENDULUM 49 

G.  MACHINES 53 

III.  PHYSICS 70 

I.  STATES  OF  MATTER 70 

A.  THREE  STATES  OF  MATTER 70 

B.  FLUIDS 72 

C.  GASES 82 

D.  LIQUIDS 90 

E.  SOLIDS 116 

II.  SOUND 120 

A.  ORIGIN  OF  SOUND       120 

B.  PROPAGATION  OF  SOUND 124 

C.  RESONANCE 141 

D.  MUSICAL  INSTRUMENTS 144 

E.  ANALYSIS  OF  SOUND 149 

III.  HEAT 157 

I.  EFFECTS  OF  HEAT 157 

A.  EXPANSION 157 

B.  MEASUREMENT  OF  TEMPERATURE 163 


Ill  CONTENTS. 

PAGB 

C.  CHANGE  OF  STATE 169 

I.  FUSION  AND  SOLIDIFICATION 169 

II.  EVAPORATION  AND  CONDENSATION    ....  172 

D.  MEASUREMENT  OF  HEAT 108 

II.  RELATIONS  BETWEEN  HEAT  AND  WORK 184 

III.  DISTRIBUTION  OF  HEAT 194 

A.  CONDUCTION 194 

B.  CONVECTION 199 

C.  RADIATION  AND  ABSORPTION 199 

IV.  LIGHT 205 

A.  RADIATION 205 

B.  REFLECTION 214 

C.  REFRACTION 217 

D.  DISPERSION 223 

E.  LENSES 229 

F.  OPTICAL  INSTRUMENTS 243 

G.  COLOR 260 

I.  THEORY  OF  COLOR 260 

II.   COLORS     PRODUCED    BY     Al.SORPTION     AND     IN- 
TERFERENCE         268 

III.  COLORS  PRODUCED  BY  POLARIZATION     .        .    .  273 

IV.  PHOSPHORESCENCE 277 

H.  CONVERSION  OF  RADIANT  ENERGY  INTO  SOUND     .  278 

V.  MAGNETISM 285 

VI.  ELECTRICITY        296 

I.  FRICTIONAL  ELECTRICITY 296 

A.  ELECTRICAL  ATTRACTIONS  AND  REPULSIONS  .    .  296 

B.  ELECTRICAL  CONDUCTION  AND  INSULATION    .    .  299 

C.  ELECTRICAL  INDUCTION 300 

D.  ELECTRICAL  POTENTIAL 308 

E.  ELECTRICAL  CHARGE 314 

F.  ELECTRICAL  CONDENSATION 320 

G.  ELECTRICAL  DISCHARGE 327 

II.  VOLTAIC  ELECTRICITY 334 

A.  DEFLECTION  OF  THE  NEEDLE 334 

B.  FLOW  OF  ELECTRICITY  THROUGH  CONDUCTORS    .  339 

C.  ELECTRO-CHEMICAL  ACTION 346 

I.  VOLTAIC  BATTERIES 346 

II.  ELECTROLYSIS 356 

D.  ELECTRO-MAGNETIC  INDUCTION 362 

E.  TELEGRAPHY 383 

I.  THE  MORSE  SYSTEM 383 

II.  DUPLEX  TELEGRAPHY 392 


CONTENTS.  IX 

PACK 

III.  QUADRUPLEX  TELEGRAPHY 399 

IV.  SUBMARINE  TELEGRAPHY -404 

F.  TRANSMISSION  OF  POWER  BY  MEANS  OF  ELF.CTRI- 

CITY 409 

G.  ELECTRO-THERMAL  ACTION 410 

H.  RADIANT  MATTER 418 

VII.  METEOROLOGY 430 

T.  CONSTITUTION  OF  THE  ATMOSPHERE 430 

II.  TEMPERATURE  OF  THE  ATMOSPHERE 434 

III.  HUMIDITY  OF  THE  ATMOSPHERE 442 

IV.  MOVEMENTS  OF  THE  ATMOSPHERE 447 

V.  CONDENSATION  IN  THE  ATMOSPHERE 455 

A.  DEW  AND  HOAR-FROST 455 

B.  FOG  AND  MIST 457 

C.  CLOUDS  AND  RAIN 460 

D.  STORMS 469 

VI.  ELECTRICAL  PHENOMENA  OF  THE  ATMOSPHERE  .    .  475 

A.  ATMOSPHERIC  ELECTRICITY 475 

B.  LIGHTNING 477 

C.  THE  AURORA 481 

VII.  OPTICAL  PHENOMENA  OF  THE  ATMOSPHERE    ...  490 

A.  REFRACTION 490 

B.  REFLECTION 496 

C.  CORON^E  AND    HALOS 497 

VIII.  THE  THREE  GREAT  CIRCULATIONS  OF  THE  GLOBE  501 


NATURAL     PHILOSOPHY. 


NATURAL    PHILOSOPHY. 


CONSTITUTION   OF   MATTER. 

1.  Molecules  and  Atoms.  —  It  is  now  generally  held  by 
physicists  that  all  bodies  are  made  up  of  very  small  dis- 
tinct particles,  called  molecules,  which  are  in  turn  made  up 
of  still  smaller  particles,  called  atoms.     These  molecules 
are  far  too  minute   to   be   seen  with   the   most  powerful 
microscope,  and  are  separated  by  spaces  many  times  as 
large    as   the   molecules   themselves.     It   has   been   esti- 
mated that  there  are  at  least  300  quintillions  of  mole- 
cules in    a  single   cubic  inch  of   air,  —  a  number  which 
would  be  represented  by  3   followed  by  twenty  ciphers. 
At  the  same  time  it  is  believed  that  the  material  molecules 
themselves  occupy  only  33^  of  the  space  in  the  cubic 
inch.     These  molecules  are   usually  made  up  of  two  or 
more  atoms,  which  are  probably  very  far  apart  compared 
with  their  size.     We  thus  gain  some  notion  of  the  extreme 
fineness  of  the  atomic  dust  of  which  matter  is  composed. 

It  has  been  found  possible  to  resolve  bodies  into  mole- 
cules, and  decompose  the  molecules  into  atoms  ;  but  it  is 
impossible  to  divide  the  atoms  by  any  means  at  our 
disposal. 

2.  Substance.  —  The  substance  of  a  body  depends  upon 
the  internal  structure  of  its  molecules.     All  the  molecules 


4  NATURAL   PHILOSOPHY. 

of  the  same  substance  are  supposed  to  be  exactly  alike. 
A  body  may  be  divided  and  subdivided  at  will,  and  the 
substance  of  every  portion  remain  the  same  so  long  as  the 
molecules  remain  intact.  The  moment  the  molecules  are 
divided,  or  their  structure  altered  by  changing  the  kind, 
number,  or  grouping  of  their  atoms,  the  substance  of  the 
body  is  changed. 

3.  The  Ether,  —  The  atoms  and  molecules  of  a  body 
are  supposed   to  be  suspended  in  a  highly  rarefied  and 
elastic  fluid,  which  fills  the  entire  universe  and  permeates 
all  bodies.     This  fluid  is  called  the  ether.      It  fills  alike 
the  spaces  among  the  atoms  and  molecules  of  bodies,  and 
among  the  planets  and  stars  of  the  universe.    It  is  without 
weight,  and  portions  of  its  mass  may  move  about  in  it  with- 
out the  slightest  friction. 

4.  Theory  of  Vortex  Atoms.  — Take  a  box  having  a  round 
hole   in   front    and   a   piece   of  stretched   cloth   for  its   back. 


Sprinkle  a  little  ammonia  on  the  bottom  of  the  box.  and  place 
in  it  a  small  dish  of  muriatic  acid,  so  as  to  fill  the  box  with  the 
fumes  of  sal-ammoniac.  On  striking  the  back  of  the  box  a  sud- 
den blow,  a  ring  of  smoke  will  issue  from  the  opening,  similar  to 
those  which  are  sometimes  seen  to  escape  from  the  smoke-stack 
of  a  locomotive.  The  box  and  rings  are  shown  in  Figure  i. 

The  rings  will  move  through  the  atmosphere  as  if  they  were 
solid  bodies.  When  two  of  these  come  into  collision  they  are 
thrown  into  energetic  vibration.  If  two  happen  to  be  moving 
in  the  same  direction,  with  their  centres  on  the  same  line,  and 


NATURAL    PHILOSOPHY.  5 

their  faces  perpendicular  to  this  line,  the  one  in  front  expands 
and  goes  slower,  and  the  one  behind  contracts  and  goes  faster, 
till  it  overtakes  and  passes  through  the  one  in  front ;  it  will  then 
begin  to  expand,  and  to  move  slower,  and  allow  the  other  one  to 
pass  through  it  in  turn;  and  so  on  alternately.  In  all  these 
changes  of  form  each  ring  preserves  its  individuality.  Each 
ring,  as  it  floats  through  the  atmosphere,  is  all  the  time  made  up 
of  precisely  the  same  particles  of  air  and  smoke,  and  these  are 
precisely  the  same  particles  of  air  and  smoke  that  were  driven 
out  of  the  box  by  the  blow  on  its  back.  It  is  not  merely  par- 
ticles of  sal-ammoniac  which  are  moving  through  the  air,  but  a 
portion  of  the  air  has  become,  as  it  were,  a  different  substance 
from  the  surrounding  air,  through  which  it  moves  very  much 
like  a  solid  body.  If  we  attempt  to  cut  one  of  these  rings,  it 
either  recedes  from  the  knife  or  wriggles  around  it,  so  as  to 
escape  without  injury. 

Every  portion  of  the  ring  is  continually  rolling  round  on  its  cir- 
cular core.  The  particles  on  the  inside  of  the  ring  are  moving 
forward,  and  those  on  the  outside  are 
moving  backward,  as  shown  by  the  arrows 
in  Figure  2.  Such  rings  are  called  vortex 
rings. 

Helmholtz  has  shown  by  mathematical 
investigation,  that,  were  such  vortex  rings 
once  started  in  a  perfect  fluid,  such  as  the 
ether  is  assumed  to  be,  they  would  always 
retain  their  individual  character,  and 
would  be  absolutely  indestructible  except  by  the  power  which 
created  them.  No  process  at  our  disposal  could  either  start 
such  a  vortex  ring  in  the  ether,  or  destroy  one  which  was 
already  in  existence.  These  vortex  rings  might  be  either  cir- 
cular in  form  or  have  any  conceivable  number  of  knots  and 
windings  upon  them. 

According  to  Sir  William  Thompson,  the  atoms  of  ordinary 
matter  are  simply  minute  vortex  rings  in  the  ether.  The  ether 
is  a  perfect  fluid,  which  fills  the  entire  universe,  and  what  we 
call  matter  is  simply  portions  of  this  ether  animated  with  vortex 
motion.  The  atoms  of  the  same  substance  are  alike,  because 
the  vortex  rings  are  all  alike  in  form  and  character.  The  atoms 


6  NATURAL   PHILOSOPHY. 

of  different  substances  differ,  because  the  vortex  rings  have 
different  forms  and  characteristics. 

5.  The  Atomic  and  Molecular  Structure  of  Bodies  analo- 
gous to  the  Molar  Structure  of  the  Sidereal  Universe.  —  The 
Sidereal  Universe  is  composed  of  stars,  each  of  which  is 
probably,  like  our  own  sun,  the  centre  of  a  solar  system 
composed  of  sun  and  planets.      The  planets  and  moons 
which  compose  a  solar  system  correspond  to  the   atoms 
which  compose  the  molecules,  and  the  solar  systems  cor- 
respond to  the  molecules  which  compose  the  body.     The 
planets  in  the  solar  system  are  sometimes  found  singly,  as 
in  the  case  of  Venus,  and  sometimes  in  groups,  as  in  the 
case  of  Jupiter.     The  same  is  true  of  the  atoms  in  the 
molecules. 

6.  All  Matter  is  Porous.  —  From  the  account  just  given 
of  the  structure  of  matter,  it  will  be  seen  that  all  matter  is 
porous,  that  is,  filled  with  spaces  which  are  not  occupied 
by  material  particles.     When  these  pores  are  too  small  to 
be  seen  with  the  microscope,  they  are  called  physical  pores. 
In  many  cases  the  pores  of  bodies  are  large  enough  to  be 
seen.     This  is  the  case  with  wood  and  many  other  sub- 
stances.    Such  pores  are  called  sensible  pores. 

7.  Atomic,  Molecular,  and  Molar  Motion.  —  Every  par- 
ticle of  matter  in  the  universe  is  in  incessant  motion.     The 
atoms  are  all  the  time  moving  about  in  the  molecules ;  the 
molecules,  in  bodies  ;  and  bodies,  in  space.    The  motion  of 
the  atoms  within  the  molecules  is  called  atomic  motion  ; 
that  of  the  molecules  in  bodies,  molecular  motion  ;  and 
that  of  bodies  in  space,  molar  motion.     Molar  motion  is 
often    called    mechanical   motion.      Sometimes   the    term 
molecular   is   applied    to   the   motion   of   both  atoms  and 
molecules. 

8.  The  Three  Great  Forces  of  Nature.  —  There  are  three 
forces  corresponding  to  the  three  orders  of  material  units. 
These  are  affinity,  cohesion,  and  gravity. 


NATURAL    PHILOSOPHY.  7 

Affinity  is  the  force  which  binds  together  the  atoms  into 
the  molecules.  It  is  therefore  an  atomic  force.  It  is  the 
strongest  of  the  forces,  but  it  acts  only  through  infinites- 
imal distances. 

Cohesion  is  a  molecular  force.  It  binds  together  the 
molecules  into  bodies.  It  is  a  weaker  force  than  affinity, 
but  is  capable  of  acting  through  greater,  though  still  insen- 
sible distances. 

Gravity  is  a  molar  force.  It  binds  together  bodies.  It 
is  the  weakest  of  the  three  forces,  but  is  capable  of  acting 
through  all  known  distances. 

Though  cohesion  binds  together  molecules,  and  gravity 
bodies,  each  probably  does  so  by  acting  directly  upon  the 
ultimate  atoms  of  which  matter  is  composed. 

9.  Elasticity.  —  Elasticity  is  the  tendency  of  a  body  to 
spring  back   to  its   original   condition  when  it  has  been 
distorted  in  any  way.     Any  distortion  whatever,  whether 
produced  by  stretching,  by  bending,  by  twisting,  by  com- 
pression, or  by  rarefaction,  is  called  a  strain.     The  force 
which  produces  the  strain  is  called  a  stress.     Elasticity  is 
always   developed  by  some  kind  of  strain.     It  is  called 
elasticity  of  traction,  of  flexure,  of  torsion,  or  of  compression, 
according  to  the  kind  of  strain  by  which  it  is  developed. 
All  bodies  are  elastic  to  some  extent,  but  usually,  when 
the  distortion  proceeds  beyond  a  certain  point,  the  elas- 
ticity of  the  body  breaks  down.     The  point  of  strain  at 
which  the  elasticity  breaks  down  is  called  the  limit  of  the 
elasticity  of  the  body. 

10.  The  Three  Orders  of  Material  Units.  —  The  three 
orders  of  material  units  are  atoms,  molecules,  and  bodies. 

n.  Chemical  Properties  of  Matter. — The  properties  of 
matter  which  grow  out  of  the  atomic  structure  of  the 
molecules  and  the  action  of  affinity  are  called  chemical 
properties. 

12.    Physical  Properties  of  Matter.  —  The  properties  of 


8  NATURAL   PHILOSOPHY. 

matter  which  grow  out  of  the  molecular  structure  of 
bodies  and  the  action  of  cohesion  are  called  physical 
properties. 

13.  The  Physical  Sciences.  —  The  physical  sciences  deal 
with  the  action  of  forces  on  material  units,  irrespective  of 
the  phenomena  of  life. 

Mechanics  deals  with  the  action  of  forces  and  the  laws  of 
motion,  irrespective  of  any  order  of  material  units. 

Astronomy  deals  with  gravity  and  molar  units. 

Physics  deals  with  cohesion,  molecules,  and  physical 
properties  of  matter. 

Chemistry  deals  with  affinity,  atoms,  and  chemical  prop- 
erties of  matter. 

Natural  Philosophy  includes  both  Mechanics  and  Phys- 
ics. In  any  treatise  on  the  various  branches  of  Physical 
Science,  it  is  impossible  to  draw  any  sharp  line  of  demar- 
cation between  them. 


II. 

MECHANICS. 
A.  DEFINITIONS.  —  UNITS.  —  NEWTON'S  LAWS  OF  MOTION. 

14.  The  Three  Fundamental  Units.  —  The  three  funda- 
mental \\mte  of  Mechanics,  from  which  all  the  other  mechan- 
ical and  .physical  units  are  derived,  are  the  unit  of  time,  the 
unit  of  length,  and  the  unit  of  mass. 

In  the  English  system  these  units  are  the  second,  the 
foot,  and  the  pound  avoirdupois.  In  the  French  system 
they  are  the  second,  the  centimetre,  and  the  gramme. 

15.  English  and  French  Units  of  Length.  —  The  English 
standard  unit  of  length  is  the  yard,  which  is  divided  into 
three  equal  parts,  called  ./£<?/.     The  foot  is  subdivided  into 
twelve  equal  parts,  called  inches.     The  yard  is  simply  the 
length  marked  on  a  certain  rod  preserved  by  the  govern- 
ment. 

The  French  standard  unit  of  length  is  the  metre.  This 
is,  theoretically,  the  forty-millionth  of  the  earth's  merid- 
ian. Practically,  it  is  the  length  of  a  rod  preserved  by  the 
French  government,  which  differs  appreciably  from  the 
theoretical  length  of  the  metre.  The  metre  is  about  3)^ 
feet.  The  metre  is  divided  into  ten,  one  hundred,  and  one 
thousand  equal  parts,  called  decimetres,  centimetres,  and 
millimetres.  Decametre,  hectometre,  and  kilometre  are,  re- 
spectively, ten  metres,  one  hundred  metres,  and  one  thou- 
sand metres.  In  the  French  system  of  units  the  prefixes 
deci,  centi,  and  milli  always  indicate  tenths,  hundredths,  and 


10  NATURAL    PHILOSOPHY. 

thousandths  of  the  unit,  while  the  prefixes  deca,  hecto,  and 
kilo  always  indicate  tens,  hundreds,  and  thousands  of  the 
units.  The  decimal  division  of  the  units,  and  the  natural 
relations  of  the  units  of  different  kinds,  render  the  French, 
or  Metric,  system  of  units  the  most  convenient  system  ever 
devised. 

For  the  purpose  of  readily  comparing  the  French  units 
of  length  with  our  familiar  English  units,  it  will  be  con- 
venient to  remember  that  a  metre  is  about  forty  inches ; 
a  decimetre,  about  four  inches ;  a  centimetre,  about  ^  of 
an  inch ;  and  a  millimetre,  about  ^  of  an  inch.  A  kilo- 
metre is  about  five  furlongs,  or  ^  of  a  mile. 

1 6.  Units  of  Surf  ace  and  of  Volume.  —  The  units  of  sur- 
face are  squares,  one  of  whose  sides  is  the  unit  of  length. 
Thus,  the  English  units  of  surface  are  the  square  yard,  the 
square  foot,  and  the  square  inch.     The  French  units  of  sur- 
face  are  the  square  metre,  the  square  decimetre,  and   the 
square  centimetre. 

The  units  of  volume  are  cubes,  one  of  whose  edges  is  the 
unit  of  length.  The  English  units  of  volume  are  the  cubic 
yard,  the  cubic  foot,  and  the  cubic  inch.  The  French  units 
of  volume  are  the  cubic  metre,  the  cubic  decimetre,  and  the 
cubic  centimetre.  The  French  unit  of  capacity  is  the  cubic 
decimetre.  It  is  called  the  litre,  and  is  equal  to  about  i  ^ 
pints. 

17.  Units  of  Mass.  —  The  mass  (A  a  body  is  the  quantity 
of  matter  which  it  contains.     The  English  unit  of  mass  is 
the  mass  of  a  certain  piece  of  metal  preserved  by  the  gov- 
ernment and  called  the  pound  avoirdupois.     It  is  divided 
into  7000  equal  parts,  called  grains.     The  French  unit  of 
mass   is  the   mass  of  a  cubic  centimetre  of  water  at  its 
maximum  density.     It  is  called  a  gramme,  and  is  equal  to 
about   15^  grains.      A  kilogramme  is  equal  to  about  2^ 
pounds. 

1 8.  Unit  of  Density. — The  density  si  a  body  is  the  quan- 


NATURAL   PHILOSOPHY.  II 

tity  of  matter  in  a  unit  of  its  volume.  The  density  of  water 
at  a  temperature  of  39°  F.  is  usually  taken  as  the  unit  of 
density. 

19.  Units  of  Velocity.  —  Velocity  is  rate  of  motion.     The 
English  unit  of  velocity  is  the  velocity  of  one  foot  a  second. 
The  French  unit  is  the  velocity  of  a  centimetre  a  second. 

When  we  speak  of  the  velocity  of  a  body  as  being  five, 
ten,  or  twenty  feet  a  second,  we  mean  that,  at  the  instant 
to  which  we  refer,  the  body  is  moving  fast  enough  to  go 
five,  ten,  or  twenty  feet  in  a  second,  provided  it  were  to 
keep  on  moving  at  the  same  rate.  It  does  not,  however, 
follow  that  it  will  actually  go  five,  ten,  or  twenty  feet  in  a 
second,  for  its  rate  may  change. 

20.  Different  Aspects  of  the  Action  of  Forces  on  Matter.  — 
Any  push  or  pull,  of  whatever  origin,  upon  any  portion  of 
matter  is  called  .a  force.     In  the    realm   of   matter  these 
forces  always  act  between  two  different  portions  of  matter. 
Thus,  affinity  is  a  pull  between  two  atoms ;  cohesion,  a  pull 
between  two  molecules  ;  and  gravity,  a  pull  between  two 
bodies.     The  action  of  a  pulling,  or  attractive,  force  may  be 
illustrated  by  fastening  two  balls  to  the  ends  of  an  india- 
rubber  cord  and  then  separating  the  balls  so  as  to  stretch 
the  cord.     The  stretched  cord  will  pull  upon  both  balls. 
The  action  of  a  pushing,  or  repulsive,  force  may  be  illus- 
trated by  placing  a  rod  of  india-rubber  between  two  balls 
and  then  crowding  the  balls  together.     The  compressed 
rubber  will  push  upon  both  balls. 

This  action  of  a  force  between  two  portions  of  matter 
takes  different  names  according  to  the  aspect  under  which 
it  is  viewed.  When  we  take  into  account  the  whole  phe- 
nomenon of  the  action  between  the  two  portions  of  matter, 
we  call  it  a  stress.  This  stress,  according  to  the  mode  in 
which  it  acts,  may  be  described  as  attraction,  repulsion,  ten- 
sion, pressure,  torsion,  etc.  When  we  confine  our  attention 
to  one  of  the  portions  of  matter,  we  see  only  one  aspect  of 


12  NATURAL    PHILOSOPHY. 

the  stress,  namely,  that  which  affects  the  portion  of  matter 
under  consideration.  This  aspect  of  the  phenomenon  we 
call,  with  reference  to  its  effect,  an  external  force,  acting 
upon  that  portion  of  matter,  and,  with  reference  to  its 
cause,  the  action  of  the  other  portion  of  matter.  The  oppo- 
site aspect  of  the  stress  is  called  the  reaction  on  the  other 
portion  of  matter. 

21.  Newton's  First  Law  of  Motion, — Every  body  perseveres 
in  its  state  of  rest  or  of  moving  uniformly  in  a  straight  line, 
unless  compelled  to  change  this  state  by  external  forces.  This 
is  Newton's  first  law  of  motion.  No  portion  of  matter  in 
the  universe,  so  far  as  known,  is  absolutely  at  rest.  Were 
there  such  a  portion  of  matter,  it  could  be  put  in  motion 
only  by  an  external  force.  Bodies  are  commonly  spoken 
of  as  at  rest  when  they  are  not  changing  their  positions 
with  respect  to  other  bodies  around  thejn.  Thus,  we  say 
that  a  body  is  at  rest  on  the  deck  of  a  steamer,  though  it 
is  really  moving  forward  with  the  steamer  ;  and  that  bodies 
are  at  rest  on  the  surface  of  the  earth,  though  they  are 
moving  along  with  the  earth.  In  all  such  cases  bodies 
are  only  relatively  at  rest.  In  common  language  bodies  are 
said  to  be  at  rest  with  respect  to  each  other  when  they  are 
all  moving  along  at  the  same  rate  and  in  the  same  direc- 
tion. When,  in  common  language,  a  body  is  said  to  be  put 
in  motion,  what  really  takes  place  is  that  its  motion  is 
changed  either  in  rate  or  direction. 

Unless  acted  upon  by  external  forces,  a  moving  body 
would  always  go  on  in  a  straight  line  and  at  a  uniform  rate. 
This  seems  to  be  contradicted  by  common  experience.  All 
moving  bodies  at  the  surface  of  the  earth  show  a  decided 
fendency  to  stop.  But  all  such  moving  bodies  are  acted 
upon  by  some  external  force  acting  as  a  resistance.  The 
chief  resistances  encountered  by  moving  bodies  are  friction 
and  resistance  of  the  atmosphere.  In  proportion  as  these 
resistances  are  diminished,  the  longer  Is  the  time  a  body 


NATURAL    PHILOSOPHY.  13 

will  continue  to  move.  A  smooth  stone  is  soon  brought  to 
rest  when  sliding  over  the  surface  of  the  earth.  The  same 
stone  will  slide  much  longer  over  the  smooth  surface  of 
ice,  where  there  is  less  friction.  A  heavy  metallic  top  in 
rapid  rotation  will  spin  for  twenty  minutes  in  the  air.  The 
same  top  will  spin  over  an  hour  in  a  vacuum.  Since  the 
time  a  body  will  continue  in  motion  increases  in  proportion 
as  the  resistance  is  diminished,  we  may  reasonably  infer 
that,  were  the  resistance  entirely  removed,  the  body  would 
continue  in  motion  forever.  To  keep  bodies  in  motion  at 
the  surface  of  the  earth,  it  is  necessary  to  bring  some  ex- 
ternal force  to  bear  on  them  sufficient  to  balance  the  resis- 
tance which  they  encounter.  There  will  be  no  change  in 
the  motion  of  a  body  when  acted  upon  by  external  forces, 
provided  these  forces  balance  one  another,  or  are  in  a 
state  of  equilibrium. 

Fig.  3. 


22.  Inertia.  —  The  tendency  of  a  body  to  persevere  in  its 
state  of  rest  or  motion  is  called  inertia.  The  inertia  of  a 
body  is  directly  proportional  to  its  mass.  This  inertia 
must  be  overcome  by  some  external  force  in  order  to  put  a 
body  in  motion,  or  to  change  the  rate  or  direction  of  its 
motion.  It  takes  time  for  a  force  to  overcome  the  inertia 
of  matter.  Hence,  when  a  body  receives  a  sudden  blow, 
the  part  of  the  body  immediately  receiving  the  blow  yields 
before  there  is  time  to  overcome  the  inertia  of  the  sur- 
rounding parts. 


14  NATURAL    PHILOSOPHY. 

There  are  many  striking  illustrations  of  inertia.  If  a 
number  of  checkers  are  piled  up  in  a  vertical  column,  one 
of  them  may  be  knocked  out  by  a  very  rapid  blow  with 
a  table  knife  without  overturning  the  column.  A  feeble 
blow  will  fail.  Stick  two  needles  into  the  ends  of  a  broom- 
stick and  rest  the  needles  on  two  glass  goblets,  as  shown 
in  Figure  3.  Strike  the  middle  of  the  stick  a  quick,  sharp 
blow  with  a  heavy  poker.  The  stick  will  break  without 
breaking  the  needles  or  the  goblets.  Here  again  a  feeble 
or  indecisive  blow  will  fail.  A  soft  body,  fired  fast  enough, 
will  hit  as  hard  as  lead.  A  tallow  candle  may  be  fired 
from  a  gun  through  a  pine  board. 


23.  Centrifugal  Force.  —  The  so-called  centrifugal  force 
is  an  illustration  of  Newton's  first  law  of  motion.  It  is 
simply  the  tendency  of  the  parts  of  a  rotating  body  to  keep 
moving  in  straight  lines.  This  tendency  increases  with  the 
speed  of  rotation.  When  a  body  is  rotating  very  rapidly, 
the  tendency  of  the  parts  to  move  in  straight  lines  is  suffi- 


NATURAL   PHILOSOPHY. 


cient  to  overcome  the  cohesion  of  the  body.  In  this  case 
the  body  will  fly  in  pieces.  If  a  stone  be  fastened  to  the 
end  of  a  string  and  twirled  rapidly  around  the  finger, 
the  tendency  of  the  stone  to  fly  off  in  a  straight  line 
may  become  sufficient  to  break  the  string.  In  this  case 
the  stone  will  start  off  in  a  line  tangent  to  the  circle  it  was 
describing  at  the  point  where  the  stone  happened  to  be. 

This  tendency  to  move  on  in  a  straight  line  must  be 
counteracted  by  the  force  acting  towards  the  centre,  in 
order  to  keep  a  body  moving  in  a  circle.  Ttfe  faster  the 
body  moves,  the  greater  the  pull  needed  to  keep  the  body 
in  its  circular  path.  The  greater  the  pull  upon  the  body 
towards  the  centre,  the  greater  the  pull  of  the  body  away 
from  the  centre.  The  pull  upon  the  body  towards  the  cen- 
tre is  called  the  centripetal  force,  and  the  pull  of  the  body 
away  from  the  centre  is  called  the  centrifugal  force.  These 
two  forces  are  only  the  two  aspects  of  the  stress  of  attrac- 
tion between  the  body  and  the  centre  about  which  it  is 
revolving. 

The  pull  of  a  revolving  body 
away  from  the  centre  may  be  il- 
lustrated by  the  pieces  of  appara- 
tus shown  in  Figures  4  and  5. 
In  the  first,  two  balls  M  and  M' 
are  placed  on  the  rod  A  B,  which 
passes  through  them.  The  rod  is 
then  put  in  rapid  rotation  by  turn- 
ing the  crank  at  the  end  of  the 
table.  The  balls  fly  apart. 

If  the  flexible  rings  of  Figure  5 
are  mounted  on  the  whirling  table 
in  place  of  the  rod,  and  put  in 
rapid  rotation,  they  will  become 
more  and  more  flattened  as  the 
speed  of  rotation  increases-  This  change  of  form  is  due 


Fig.  5. 


l6  NATURAL   PHILOSOPHY. 

to  the  pull  of  each  part  of  the  rings  away  from  the  cen- 
tral axis.  The  pull  will  be  greatest  at  the  central  point 
of  the  rings,  because  this  part  is  moving  at  the  highest 
speed.  It  was  in  this  way  that  the  earth  became  flattened 
at  the  poles  while  in  the  fluid  state. 

The  centrifugal  railway  (Figure  6)  shows  a  curious  effect 
of  this  outward  pull.  A  carriage  starting  from  A  descends 
the  incline  to  JS,  passes  up  around  the  circle  C,  and  then 
up  the  incline  to  D.  The  outward  pull  of  the  carriage  due 
to  its  velocity  is  sufficient  to  keep  it  against  the  rails  while 
passing  around  the  circle,  though  it  is  part  of  the  time 
travelling  bottom  up. 

Fig.  6. 


24.  Stabilitv  of  a  Rotating  Body,  —  The  tendency  of  the 
particles  of  matter  to  keep  moving  in  the  same  plane  ex- 
plains why  a  top  will  stand  upright  so  long  as  it  is  spinning 
rapidly,  though  it  topples  over  at  once  as  soon  as  it  comes 
to  rest.  For  the  same  reason  a  bicycle  is  not  easily  over- 
turned while  its  large  wheel  is  in  rapid  rotation. 

2  5 .  External  Forces  tend  to  put  Bodies  in  Motion  or  to 
change  their  Velocities. —  Suppose  a  rubber  cord  fastened  at 
one  end  to  a  body,  not  acted  on  by  any  other  force  than 
the  tension  of  the  cord,  and  suppose  the  cord  to  be  kept 
stretched  to  the  same  extent  all  of  the  time,  so  as  to  exert 
a  uniform  pull  upon  the  body.  The  body  will  begin  to  move 
in  the  direction  of  the  pull,  and  will  move  faster  and  faster 
the  longer  the  pull  continues.  The  body  will  gain  the  same 
amount  of  velocity  each  second.  If  it  were  moving  at  the 


NATURAL   PHILOSOPHY.  17 

rate  of  two  feet  a  second  at  the  end  of  the  first  second,  it 
will  be  moving  at  the  rate  of  four  feet  a  second  at  the  end 
of  the  second  second,  at  the  rate  of  six  feet  a  second  at 
the  end  of  the  third  second,  and  so  on. 

26.  Units  of  Force. —  Forces  may  be  measured  either 
by  the  pressure  which  they  would  produce  or  by  the  rate 
at  which  they  would  increase  the  velocity  of  a  mass  of 
matter. 

In  the  former  case  the  unit  of  force  is  the  force  of 
gravity  on  a  unit  of  mass.  In  the  English  system  it  is  the 
force  of  gravity  on  a  mass  of  a  pound  or  a  grain,  and  is 
called  a. pound  or  a  grain.  In  the  French  system  it  is  the 
force  of  gravity  on  a  mass  of  a  gramme,  and  is  called  a 
gramme.  These  units  are  called  gravitation  units  ;  and 
since  they  depend  upon  the  intensity  of  gravity,  they  are 
variable,  changing  with  the  intensity  of  gravity  at  different 
places  on  the  surface  of  the  earth,  and  at  different  eleva- 
tions above  the  surface. 

In  the  latter  case  the  unit  of  force  is  the  force  that  will 
impart  to  a  unit  of  mass  a  unit  of  Velocity  in  a  unit  of  time. 
In  the  English  system  it  is  the  force  that  will  impart  to  a 
mass  of  a  pound  a  velocity  of  a  foot  in  a  second.  It  is 
called  z.poundal.  At  Greenwich  it  takes  32.2  poundals  of 
force  to  hold  up  a  pound. 

A  system  of  absolute  measurement  has  been  devised  in 
England,  and  adopted  by  the  British  Association.  The 
units  of  this  system  are  all  based  upon  the  centimetre, 
gramme,  and  second,  as  the  three  fundamental  units  of 
length,  mass,  and  time.  This  system  of  measurement  is 
called  the  centimetre-gramme-second  system,  or  more  briefly, 
the  C.  G.  S.  system.  Its  units  are  called  the  centimetre- 
gramme-second  units,  or  more  briefly,  the  C.  G.  S.  units. 

In  the  C.  G.  S.  system  the  unit  of  force  is  the  force  that 
will  impart  to  a  mass  of  a  gramme  a  velocity  of  one  centime- 
tre a  second.  It  is  called  a  dyne.  It  takes  445,000  dynes  of 


1 8  NATURAL   PHILOSOPHY. 

force  to  hold  up  a  pound  at  Greenwich.  These  units  are 
independent  of  gravity,  and  are  invariable.  They  are  called 
absolute  units.  . 

27.  The  Impulse  of  Force.  —  The  effect  of  a  force  in  pro- 
ducing motion  is  directly  proportional  to  its  intensity  and 
the  time  during  which  it  acts.    The  product  of  the  intensity 
of  a  force  and  the  time  during  which  it  acts  is  called  the 
impulse  of  the  force. 

28.  Momentum.  —  The  motion  of  a  body  is  measured  by 
the  mass  and  the  velocity  of  the  body,  and  is  directly  pro- 
portional to  the  two.     If  two  bodies  have  equal  velocities, 
but  one  of  them  has  five  times  the  mass  of  the  other,  it  is 
said  to  have  five  times  the  motion.     Or,  if  two  bodies  have 
equal  masses,  and  one  of  them  has  five  times  the  velocity  of 
the  other,  it  is  said  to  have  five  times  the  motion  of  the 
other.     The  product  of  the  mass  of  a  body  and  its  velocity 
is  called  the  momentum  of  the  body. 

29.  Newton's  Second  Law  of  Motion.  —  Change  of  motion 
is  proportional  to  the  impressed  force,  and  takes  place  in  the 
direction  in  which  the  force  acts.      This  is  Newton's  second 
law  of  motion. 

By  motion,  as  here  used,  Newton  means  what  is  now  called 
momentum,  in  which  the  quantity  of  matter  moved  is  taken 
into  account  as  well  as  the  rate  at  which  it  travels.  For 
instance,  there  would  be  the  same  change  of  motion  whether 
the  velocity  of  four  pounds  was  changed  one  foot  a  second 
or  the  velocity  of  one  pound  four  feet  a  second.  In  either 
case  the  change  of  momentum  would  be  four. 

By  impressed  force  Newton  means  what  is  now  called 
impulse,  in  which  the  time  the  force  acts  is  taken  into  account 
as  well  as  the  intensity  of  the  force.  Thus,  the  impulse,  or 
impressed  force,  would  be  the  same  whether  a  force  of  a 
poundal  were  acting  five  seconds  or  a  force  of  five  poundals 
was  acting  one  second.  In  either  case  the  impulse,  or  im- 
pressed force,  would  be  five. 


NATURAL   PHILOSOPHY.  19 

Newton's  second  law,  stated  in  terms  of  momentum, 
would  be  :  The  change  of  momentum  of  a  body  is  numeri- 
cally equal  to  tlie  impulse  whic/i  produced  it,  and  is  in  the  same 
direction. 

An  unbalanced  external  force  acting  upon  a  body  always 
changes  the  velocity  of  the  body  in  the  direction  in  which 
it  acts.  This  change  of  velocity  is  called  acceleration.  The 
acceleration  produced  in  a  given  time  by  a  force  acting  upon 
a  body  is  precisely  the  same  whether  the  body  is  at  first  at 
rest  or  in  motion,  or  whether  the  force  is  acting  alone  or 
with  other  forces. 

Imagine  a  platform,  and  upon  it  a  little  iron  ball,  and  5  feet 
from  the  ball  a  magnet  strong  enough  to  pull  the  ball  3  feet 
towards  itself  in  a  second,  and  to  give  it  a  velocity  of  6  feet  in 
the  same  time.  Imagine  the  ball,  magnet,  and  platform  placed 
within  a  car,  which  is  at  first  standing  still.  Suppose  the  mag- 
net placed  on  the  platform  5  feet  from  the  ball  in  any  direc- 
tion whatever,  it  will  draw  the  ball  3  feet  towards  itself  in  a 
second,  and  give  it  an  acceleration  of  6  feet  in  the  direction  of 
the  pull.  Now  suppose  the  car  moving  forward  at  the  uniform 
rate  of  12  feet  a  second.  The  ball  will  of  course  be  moving 
forward  at  the  same  rate.  If  now  the  magnet  is  placed  on 
the  platform  5  feet  from  the  ball,  as  before,  it  will  draw  the  ball 
3  feet  towards  itself,  and  give  it  an  acceleration  of  6  feet  a 
second  in  the  direction  of  the  pull,  as  before.  If  the  magnet  is 
placed  in  front  of  the  ball,  the  acceleration  of  6  feet  will  be  in 
the  direction  of  the  original  motion  of  the  ball,  and  the  forward 
velocity  of  the  ball  at  the  end  of  the  second  will  be  12  +  6=  18 
feet  a  second.  If  the  magnet  is  placed  behind  the  ball,  the  ac- 
celeration of  6  feet  will  be  in  the  opposite  direction  to  the  origi- 
nal motion,  and  the  forward  velocity  of  the  ball  at  the  end  of  the 
second  will  be  12  —  6  =  6  feet  a  second.  If  the  magnet  is 
placed  at  the  side  of  the  ball,  the  acceleration  will  be  to  the  right 
or  left  of  the  direction  of  the  original  motion  of  the  ball,  and  at 
the  end  of  the  second  the  ball  will  have  a  forward  velocity  of 
12  feet  a  second,  and  a  lateral  velocity  in  the  direction  of  the  pull 
of  the  magnet  of  6  feet  a  second. 


20  NATURAL    PHILOSOPHY. 

When  the  acceleration  is  opposed  to  the  original  motion  of  a 
body,  it  is  usually  called  a  retardation. 

Imagine  the  platform  with  the  ball  and  magnet  on  it  dropped 
over  a  precipice.  The  ball  will  then  be  acted  upon  by  two  forces, 
both  of  which  will  give  it  an  acceleration.  Gravity  will  draw  it 
16  feet  towards  the  earth,  and  give  it  an  acceleration  of  32  feet 
in  that  direction  in  a  second,  and  the  magnet  will  draw  it  3  feet 
towards  itself,  and  give  it  an  acceleration  of  6  feet  in  this  direc- 
tion in  a  second.  Each  force  has  drawn  the  ball  the  same  dis- 
tance, and  given  it  the  same  acceleration  in  the  direction  in  which 
it  acts  as  it  would  have  done  had  it  acted  alone. 

Newton's  second  law,  stated  in  terms  of  acceleration, 
would  be  :  When  any  number  of  forces  act  upon  a  body,  the 
acceleration  due  to  each  force  is  the  same  in  magnitude  and 
direction  as  if  the  others  had  not  been  in  action. 

The  total  acceleration  produced  by  the  action  of  a  force 
is  directly  proportional  to  the  impulse  of  the  force,  and  in- 
versely proportional  to  the  mass  acted  upon.  A  force  of 
40  poundals  acting  for  20  seconds  upon  a  mass  of  50  pounds 
would  produce  an  acceleration  of  40  X  20  -j-  50  =  16  feet. 
A  force  of  300  dynes  acting  80  seconds  upon  200  grammes 
would  produce  an  acceleration  of  300  X  80  -r-  200=  120 
centimetres. 

The  total  change  of  momentum  produced  by  the  action 
of  a  force  is  numerically  equal  to  the  impulse  of  the  force. 
A  force  of  40  poundals  acting  30  seconds  would  produce  a 
change  of  momentum  equal  to  40  X  3°  =  I20°  units  (Eng~ 
lish).  A  force  of  250  dynes  acting  20  seconds  would  pro- 
duce a  change  of  momentum  equal  to  250  X  20  =  5000 
units  (C.  G.  S.). 

QUESTIONS  ON  NEWTON'S  SECOND  LAW. 

\.  What  acceleration  would  be  produced  by  a  force  of  30 
poundals  acting  on  a  mass  of  80  pounds  for  70  seconds  ? 

2.  What  acceleration  would  be  produced  by  a  force  of  96 
poundals  acting  upon  a  mass  of  36  pounds  for  500  seconds  ? 


NATURAL    PHILOSOPHY.  21 

3.  What  acceleration  would  be  produced  by  the  action  of  a 
force  of  720  dynes  on  a  mass  of  300  grammes  for  40  seconds? 

4.  What  acceleration  would  be  produced  by  a  force  of  240 
dynes  acting  on  a  mass  of  3  kilogrammes  for  3  minutes? 

5.  What  must  be  the  intensity  of  a  force  that  would  give 
90  pounds  an  acceleration  of  1000  feet  in  20  seconds  ? 

6.  What  must  be  the  intensity  of  a  force  that  would  give  a 
mass  of  80  grammes  an  acceleration  of  50  metres  in  2  minutes  ? 

7.  What  must  be  the  mass  of  a  body  to  which  a  force  of  60 
poundals  would  give  an  acceleration  of  500  feet  in  30  seconds  ? 

8.  What  must  be  the  mass  of  a  body  to  which  a  force  of  500 
dynes  would  give  an  acceleration  of  8  decimetres  in  8  seconds  ? 

9.  What  momentum  would  be  imparted  to  a  body  by  a  force 
of  70  poundals  in  90  seconds  ? 

10.  What  momentum  would  be  imparted  to  a  body  by  a  force 
of  350  dynes  in  75  seconds  ? 

1 1.  What  force  would  be  needed  to  change  the  momentum  of 
a  body  300  units  (English)  in  9  seconds? 

12.  What  force  would  be  needed  to  change  the  momentum 
of  a  body  900  units  (C.  G.  S.)  in  60  seconds  ? 

13.  How  long  will  it  take  a  force  of  120  poundals  to  impart  a 
momentum  of  700  units  to  a  body  ? 

14.  How  long  would  it  take  a  force  of  600  dynes  to  impart 
a  momentum  of  19,000  units  to  a  body  ? 

15.  How  long  would  it  take  a  force  of  20  poundals,  acting  in 
the  opposite  direction  to  the  motion  of  the  body,  to  stop  a  body 
having  a  momentum  of  300  units  ? 

16.  How  long  would  it  take  a  force  of  80  dynes,  acting  in  the 
opposite  direction  to  the  motion  of  the  body,  to  stop  a  body  hav- 
ing 1,000  units  of  momentum  ? 

17.  How  long  would  it  take  a  force  of  a  poundal,  acting  in 
the  opposite  direction  to  the  motion  of  the  body,  to  stop  a  body 
having  a  momentum  of  960  units  ? 

1 8.  How  long  would  it  take  a  force  of  a  dyne,  acting  in  the 
opposite  direction  to  the  motion  of  the  body,  to  stop  a  body  hav- 
ing a  momentum  of  572  units  ? 

19.  How  long  would  it  take  a  force  of  40  poundals,  acting  in 
the  opposite  direction  to  the  motion  of  the  body,  to  stop  a  mass 
of  50  pounds  having  a  velocity  of  80  feet  a  second  ? 


22  NATURAL    PHILOSOPHY. 

20.  How  long  would  it  take  300  dynes  of  force,  acting  in  the 
opposite  direction  to  the  motion  of  the  body,  to  stop  a  mass  of 
90  grammes  with  a  velocity  of  600  centimetres  a  second  ? 

30.  Parallelogram  of  Motion. — To  find  the  path  of  a 
body  A  (Figure  7)  acted  on  by  two  forces  at  the  same  time, 

Fig  7  draw  A  B  to  represent  the  path  the  body 

would  have  taken  had  it  been  acted  on 
by  the  first  force  alone,  and  A  C  to  repre- 
sent the  path  it  would  have  taken  had  it 
been  acted  on  by  the  other  force  alone. 
Through  B  draw  BD  parallel  to  AC, 
and  through  C  draw  CD  parallel  to 
AB,  so  as  to  complete  the  parallelogram 
AB  DC.  Draw  the  diagonal  A  D  This 

diagonal  will  represent  the  path  taken  by  the  body  when 

acted  upon  by  both  forces  together. 

31.  Newton's  Third  Law  of  Motion.  —  Newton's  third 
law  of  motion  is  as  follows :  Reaction  is  always  equal  and 
opposite  to  action  ;  that  is  to  say,  the  actions  of  two  bodies  upon 
each  other  are  always  equal  and  in  opposite  directions. 

This  law  simply  states  the  fact  that  a  force  always  acts 
upon  two  portions  of  matter,  and  that  the  stress,  whether 
that  of  tension  or  pressure,  is  equal  upon  both  portions. 
A  stone  raised  from  the  earth  attracts  the  earth  just  as 
much  as  the  earth  attracts  the  stone.  Gravity  really  acts 
as  a  stress  of  tension  between  the  two,  and  pulls  them 
equally  but  in  opposite  directions.  When  the  stone  falls 
the  earth  moves  up  to  meet  it.  When  the  two  meet  they 
have  each  the  same  momentum,  but  the  earth,  owing  to  its 
great  mass,  has  only  a  very  small  velocity.  When  a  cannon 
is  fired,  the  ignited  powder  pushes  back  upon  the  cannon 
just  as  hard  as  it  pushes  forward  on  the  ball.  Were  the 
cannon  as  free  to  move  as  the  ball,  it  would  start  back,  or 
recoil,  with  the  same  momentum  that  the  ball  starts  forward 
with,  but  of  course  with  a  less  velocity. 


NATURAL    PHILOSOPHY.  23 

32.  Collision  of  Elastic  Bodies. — We  have  an  illustra- 
tion of   action    and    reaction    in    the   collision   of   elastic 
bodies.      Place  two  ivory  balls  of  exactly  the  same  size 
at   the   centre    of  Fig.  8. 

the  curved  rail- 
way (Figure  8). 
Move  one  of  the 
balls  up  the  rail- 
way on  one  side,  ^ rTYYYT)O 

and  let  it  roll 
back  against  the 
one  at  rest.  There 

win  be  a  slight     >> nrnmno - 

strain  of  compres-  \  A  A  A  A  A-A-^ 

sion  when  the  balls  strike,  and  this  will  develop  a  stress 
of  elasticity  between  the  balls  which  will  act  equally  upon 
them  and  in  opposite  directions.  This  stress  will  stop 
the  first  ball,  and  start  the  second  off  with  the  velocity  the 
first  had  on  striking  it. 

Place  several  ivory  balls  of  the  same  size  on  the  centre 
of  the  track  (Figure  8),  and  allow  the  first  ball  to  roll 
against  the  end  of  the  line.  «A11  the  balls  will  remain  at 
rest  except  the  last,  which  will  be  shot  up  the  track.  In 
this  case  the  strain  of  compression  and  stress  of  elasticity 
have  been  propagated  along  the  line  from  ball  to  ball. 
Each  ball  has  been  compressed  a  little  in  turn,  and  in 
recovering  itself  has  pushed  upon  the  ball  behind  it  enough 
to  stop  it,  and  upon  the  one  in  front  enough  to  flatten  it  a 
little.  Each  ball  was  kept  from  moving  forward  by  the 
reaction  of  the  ball  in  front,  except  the  last. 

B.   WORK  AND  ENERGY. 

33.  Work.  —  Work  is  said  to  be  done  when  anything  is 
moved  against  resistance.     We  may  consider  work  either 
with  reference  to  the  force  that  moves  the  body  or  with 


24  NATURAL    PHILOSOPHY. 

reference  to"  the  resistance  overcome.  When  we  think  of 
the  force  as  moving  the  body,  we  say  that  work  is  done  by 
the/0ra?  upon  the  body.  When  we  think  of  the  resistance 
as  overcome  by  the  body,  we  say  that  work  is  done  by  the 
body  upon  the  resistance.  When  we  think  of  the  resist- 
ance as  impeding  the  motion  of  the  body,  we  say  that  work 
is  done  by  the  resistance  upon  the  body.  These  terms 
apply  to  different  aspects  of  the  same  work.  Thus,  when 
we  raise  a  weight,  in  winding  up  a  clock,  we  may  say  that 
work  is  done  by  the  force  used  upon  the  weight,  or  by  the 
weight  upon  or  against  gravity,  or  by  gravity  upon  the 
weight.  The  amount  of  work  done  is  the  same,  in  what- 
ever aspect  we  view  it.  When  the  clock  weight  runs 
down  again,  we  may  say  that  work  is  done  by  gravity  upon 
the  weight,  or  by  the  weight  upon  the  resistance  of  the 
wheels,  or  by  the  resistance  of  the  wheels  upon  the  weight, 
according  to  the  aspect  in  which  we  view  the  work.  When 
a  weight  is  allowed  to  fall  freely  to  the  earth,  the  work 
done  is  that  of  increasing  the  velocity  of  the  body.  In 
this  case  work  is  done  by  gravity  upon  the  body,  and  by 
the  body  upon  its  inertia. 

Work  is  done  in  every  case  in  which  the  velocity  of  a 
body  is  changed,  for  the  inertia  of  the  body  always  resists 
this  change. 

34.  Units  of  Work.  —  The  unit  of  work  is  the  work 
done  in  moving  anything  a  unit  of  distance  against  a  unit 
of  resistance,  or  by  a  unit  of  force  acting  through  a  unit  of 
distance.  A  resistance  is,  of  course,  merely  the  opposing 
action  of  some  force,  and  is  measured  in  poundals  or 
dynes.  The  English  unit  of  work  is  the  work  done  in 
moving  a  mass  one  foot  against  a  poundal  of  resistance,  or 
by  a  force  of  a  poundal  acting  one  foot.  It  is  called  zfoot- 
poundal.  The  C.  G.  S.  unit  of  work  is  the  work  done  in 
moving  a  mass  one  centimetre  against  a  dyne  of  resist- 
ance, or  by  the  force  of  a  dyne  acting  one  centimetre.  It 


NATURAL    PHILOSOPHY.  25 

is  called  an  erg.      There   are  421,393.8  ergs   in  a  foot- 
poundal.     These  are  absolute  units. 

The  gravitation  unit  of  work  is  the  work  done  in  raising 
a  unit  of  mass  a  unit  in  height.  The  English  unit  of  work 
is  the  work  done  in  raising  a  pound  one  foot  high.  It  is 
called  a  foot-pound.  It  varies  with  the  force  of  gravity  in 
different  parts  of  the  earth  and  at  different  elevations. 
At  Greenwich  there  are  32.2  foot-poundals  in  a  foot- 
pound. 

35.  The  Amount  of  Work  done  in  stopping  a  Moving  Body. 
—  If  we  let  M  represent  the  number  of  units  of  mass  in  a  body, 
and  V  the  number  of  units  in  its  velocity,  then  M  V  will  repre- 
sent its  momentum.     This  is  the  usual  formula  for  momentum. 

Now  it  will  take  a  unit  force  acting  against  the  motion  of  a 
body  M  V seconds  to  stop  the  body,  for  the  force  would  dimin- 
ish the  momentum  of  the  body  one  unit  each  second,  and  the 
body  has  M  V units  of  momentum.  Suppose  the  body  has  7 
units  of  mass  and  8  units  of  velocity,  it  will  have  56  units  of 
momentum,  and  it  will  take  a  unit  force  56  seconds  to  stop  the 
body. 

As  the  force  is  acting  against  the  motion  of  the  body,  its 
velocity  will  be  uniformly  diminished  till  it  becomes  zero.  The 
mean  velocity  during  the  time  the  force  is  acting  is  therefore  ^ 
of  the  velocity  it  had  at  first,  and  the  distance  the  body  goes 
will  be  equal  to  the  product  of  the  time  and  the  mean  velocity. 
In  the  example  above,  the  mean  velocity  is  8  -f-  2  =  4,  and  the 
distance  is  56  X  4  =  224  feet. 

In  the  general  case,  the  time  it  would  take  a  unit  force  to  stop 
the  body  is  M  V  seconds,  the  mean  velocity  during  the  time 
is  l/z  V,  and  the  distance  through  which  the  force  must  act  to 
stop  the  body  is  M  V  X  Yt  V  =  Yt  M  V1.  In  other  words,  the 
distance  a  unit  force  must  act  to  stop  a  moving  body  is  equal  to 
the  product  of  the  momentum  of  the  body  and  ^  of  its  velocity. 
From  the  definition  of  a  unit  of  work,  it  will  be  seen  that  this  is 
the  number  of  units  of  work  done  in  stopping  the  body. 

36.  The  Amount  of  Work  done  in  imparting  to  a  Body  any 
Acceleration.  —  The  time  it  will  take  a  unit  force  to  impart  an 


26  NATURAL    PHILOSOPHY. 

acceleration  v  will  be  equal  to  the  number  of  units  of  momen- 
tum imparted  to  the  body.  Suppose  the  mass  of  the  body  is  5 
and  the  acceleration  imparted  to  it  is  8  feet  a  second  ;  the 
momentum  imparted  to  the  body  will  be  5  X  8  =  40  units.  It 
would  take  a  unit  force  40  seconds  to  impart  this  momentum. 
The  work  done  in  imparting  this  momentum  is  precisely  the 
same  whether  the  body  were  originally  at  rest  or  in  motion. 
Suppose  the  body  originally  at  rest.  The  mean  velocity  during 
40  seconds  would  be  8-7-2  =  4;  and  the  distance  the  force 
would  have  to  act  to  impart  the  acceleration  would  be  equal  to 
the  space  passed  over  by  the  body,  or  40  X  4  =  160.  It  would 
therefore  require  160  units  of  work  to  impart  to  a  mass  of 
5  pounds  an  acceleration  of  8  feet  a  second.  In  general,  the 
work  done  in  producing  any  acceleration  or  retardation  is  equal 
to  the  product  of  the  change  of  momentum  and  l/2  the  acceleration 
or  retardation.  Let  in  v  represent  the  change  of  momentum, 
and  v  represent  the  acceleration  or  retardation.  Then  the  work 
done  in  producing  the  acceleration  or  retardation  will  be  equal 
to  y2  m  ir. 

QUESTIONS  ON  WORK. 

21.  How  long  would  it  take  a  poundal  of  force  to  stop  a  mass 
of  50  pounds  moving  at  the  rate  of  80  feet  a  second  ? 

22.  How  long  would  it  take  a  dyne  of  force  to  stop  a  mass  of 
200  grammes  moving  at  the  rate  of  800  centimetres  a  second  ? 

23.  How  long  would  it  take  a  force  of  15  poundals  to  stop  a 
mass  of  500  pounds  moving  with  a  velocity  of  90  feet  a  second  ? 

24.  How  long  would  it  take  a  force  of  500  dynes  to  stop  a 
mass  of  900  grammes  moving  with  a  velocity  of  600  centimetres 
a  second  ? 

25.  Through  what  distance  would  a  poundal  of  force  have  to 
act  to  stop  a  mass  of  30  pounds  moving  with  a  velocity  of  70 
feet  a  second  ? 

26.  Through  what  distance  would  a  dyne  of  force  have  to  act 
to  stop  a  mass  of  280  grammes  moving  with  a  velocity  of  700 
centimetres  a  second? 

27.  Through  what  distance  would  a  force  of  20  poundals  have 
to  act  to  stop  a  mass  of  250  pounds  moving  with  a  velocity  of 
60  feet  a  second? 


NATURAL    PHILOSOPHY.  2f 

28.  Through  what  distance  would  a  force  of  75  dynes  have  to 
act  to  stop  a  mass  of  80  grammes  moving  with  a  velocity  of 
1200  centimetres  a  second  ? 

29.  How  many  foot-poundals  of  work  would  be  done  in  stop- 
ping a  mass  of  90  pounds  moving  with  a  velocity  of  500  feet  a 
second  ? 

30.  How  many  ergs  of  work  would  be  done  in  stopping  a 
mass  of  600  grammes  moving  with  a  velocity  of  200  centimetres 
a  second?  • 

31.  How  far  would  a  poundal  of  force  have  to  act  to  impart  to 
a  mass  of  80  pounds  an  acceleration  of  40  feet  a  second  ? 

32.  How  far  would  a  dyne  of  force  have  to  act  to  impart  to 
a  mass  of  800  grammes  an  acceleration  of  300  centimetres  a 
second  ? 

33.  How  many  foot-poundals  of  work  would  be  done  by  a 
force  in  imparting  to  a  mass  of  400  pounds  an  acceleration  of 
20  feet  a  second  ? 

34.  How  many  ergs  of  work  would  be  done  by  a  force  in 
imparting  to  a  mass  of  90  grammes  an  acceleration  of  700  centi- 
metres a  second  ? 

35.  How  many  foot-poundals  of  work   must  be  done  by  a 
resistance  to  retard  the  velocity  of  a  mass  of  75  pounds  200  feet 
a  second 

36.  How  many  ergs  of  work  must  be  done  by  a  resistance  to 
retard  the  velocity  of  a  mass  of   1500  grammes  900  centimetres 
a  second  ? 

37.  Energy.  —  Energy  is  the  capacity  for  doing  work. 
It  is  measured  in  the  same  units  as  work,  a  unit  of  energy 
being  the  capacity  for  doing  a  unit  of  work.    Thus,  we  may 
speak  of  so  many  foot-poundals,  or  of  so  many  ergs,  of 
energy. 

The  force  that  tends  to  stop  a  moving  body  acts  upon 
it  as  a  resistance,  and,  as  we  have  seen,  every  moving 
body  has  the  power  to  overcome  this  resistance  through  a 
greater  or  less  distance  according  to  its  momentum  and 
velocity.  Hence  every  moving  body  has  a  capacity  for 
doing  work,  or  eticrgv.  A  body  which  is  not  in  motion 


28  NATURAL   PHILOSOPHY. 

may  have  a  capacity  for  doing  work  growing  out  of  its  con- 
dition with  respect  to  some  force.  Thus,  a  raised  weight 
has  the  ability  to  drive  a  clock,  compressed  steam  the 
ability  to  drive  a  locomotive,  and  a  coiled  spring  to  drive 
a  watch. 

38.  Position  of  Advantage.  —  A  body  is  said  to  have  a 
position  of  advantage  with  respect  to  a  force  when  it  is  so 
situated  that  it  is  possible  for  that  force  to  put  it  in  motion. 
A  weight  raised  from  the  earth  has  a  position  of  advantage 
with  respect  to  gravity,  since  it  is  possible  for  gravity  to 
put  it  in  motion  by  pulling  it  to  the  earth  again.     For  a 
similar  reason  molecules  when  separated  from  each  other 
have  positions  of  advantage  with  respect  to  cohesion  ;  and 
atoms  when  separated  from  each  other,  with  respect  to 
affinity.     A  strained  body  has  a  position  of  advantage  with 
respect  to  elasticity. 

39.  Kinetic  Energy.  —  The  energy  of  motion  is  called 
kinetic  energy. 

The  kinetic  energy  of  a  body  is  equal  to  the  product  of  the 
momentum  of  the  body  and  %  its  velocity ;  that  is,  the  kinetic 
energy  of  a  body  equals  M  V  X  }4  V=  Yt  M  V'2-  For  we  have 
seen  that  this  represents  the  work  that  must  be  done  by  a  force 
to  stop  a  body.  Now  we  may  regard  this  work  either  as  work 
done  by  the  force  acting  as  a  resistance  upon  the  body  or  by  the 
body  upon  the  resistance. 

40.  Potential  Energy.  —  The  energy  of  position  is  called 
potential  energy.     It  is  universally  true  that  a  body,  in  re- 
turning from  a  position  of  advantage  to  its  original  posi- 
tion, does  exactly  the  same  amount  of  work  that  was  done 
upon  it  in  putting  it  in  its  position  of  advantage.     Thus, 
to  raise  a  pound  weight   12  feet  high  required  12  foot- 
pounds of  work.     The  same  weig"ht  in  falling  12  feet  will 
do  12  foot-pounds  of  work.     If  it  take  300  ergs  of  work  to 
coil  a  spring,  the  spring  in  uncoiling  will  do  300  ergs  of 
work.      Hence  the  potential  energy  of  a  body  is  equal 


NATURAL   PHILOSOPHY.  29 

to  the  work  required  to  put  the  body  in   its  position   of 
advantage. 

QUESTIONS  ON  ENERGY. 

37.  How  many  foot-poundals  of  energy  has  a  mass  of  2500 
pounds  with  a  velocity  of  5000  feet  a  second  ? 

38.  How  many  ergs  of  energy  has  a  mass  of  8965  grammes 
with  a  velocity  of  8000  centimetres  a  second  ? 

39.  How  many  foot-poundals  of  energy  has  a  mass  of  3  tons 
with  a  velocity  of  500  feet  a  second  ? 

40.  How  many  ergs  of  energy  has  a  mass  of  9  kilogrammes 
with  -a  velocity  of  8  metres  a  second  ? 

C.    COMPOSITION  AND  RESOLUTION  OF  FORCES. 

41.  Representation  of  Forces  by  Lines.  —  A  force  may  be 
completely  represented  by  a  line  ;   the  length  of  the  line 
representing  the  intensity  of  the  force,  the  direction  of  the 
line  the  direction  in  which  the  force  acts,  and  one  end  (A  the 
line  the/0/«/  of  application  of  the  force. 

42.  Resultant  and  Component  Forces. — There  is  usually 
some  one  force  that  would  have  the  same  effect  upon  a 
body,  in   producing  pressure  or  motion,   as   that  of   the 
several  forces  that  may  be  acting  together  upon  it.     This 
force  is  called  the  resultant  of  these  forces,  and  they  are 
called  its  components. 

43.  Composition  and  Resolution  of  Forces.  —  The  combin- 
ing of  several  forces  into  one  resultant  is  called  the  compo- 
sition of  forces ;  and  the  decomposition  of  one  force  into 
two  or  more  components,  the  resolution  of  forces.     In  the 
composition  and  resolution  of  forces  it  is  necessary  to  find 
the  intensity,  the  direction,  and  the  point  of  application  of 
the  resultant  or  components. 

44.  The  Composition  of  Forces  acting  along  the  Same  Line 
upon  a  Point.  —  When  several  forces  act  in  the  same  direction 
along  a  line  on  a  point,  their  resultant  would  have  the  intensity 
of  the  sum  of  its  components,  the  direction  of  each  component, 
and  the  same  point  of  application  as  the  components. 


30  NATURAL    PHILOSOPHY. 

When  some  of  the  forces  are  acting  on  the  point  in  one 
direction  and  others  in  the  opposite  direction,  the  intensity  of 
the  resultant  will  be  equal  to  the  difference  between  the,  sums 
of  the  intensities  of  the  two  sets  of  forces,  the  direction  of  the 
resultant  will  be  the  direction  of  the  larger  set  of  components, 
and  the  point  of  application  will  be  the  same  as  that  of  its 
components. 

45.    Composition  of  two  Oblique  Forces  acting  upon  a  Point. 
—  Let  two  oblique  forces    A  B  and  A  C  (Figure  9)  be  acting 
Fig.  9.  upon  the  point  A  in  the  direction 

JP  indicated  by  the  arrows.  Through 

B  draw  the  line  BD  parallel  to 
AC;  and  through  C,  the  line 
^\  C  E  parallel  to  A  B,  so  as  to  form 
D^  the  parallelogram  ABRC.  The 
diagonal  A  R  of  this  parallelo- 
gram will  be  the  resultant  of  these 
two  forces.  The  above  method  is  called  that  of  the  parallelo- 
gram of  forces. 

If   a  force  A  G  (Figure   10),  having  the  intensity  of  the  re- 
sultant   A  R,   but    the    opposite 
direction,  were    applied  to  A,  it 
would  balance  this  resultant,  and, 
^K  therefore,    its    components    A  B 
^   ^  and  A  C. 

c'  The  fact  that  the  resultant  of 

forces  may  be  balanced  by  an  equal  force  applied  to  the  same 
point  in  the  opposite  direction  enables  us  to  find  the  resultant 
of  forces  experimentally,  and  so  to  verify  the  above  method. 
The  apparatus  for  this  experimental  determination  is  shown  in 
Figure  n.  ABDC  is  a  parallelogram  jointed  at  its  four 
corners.  Cords  pass  from  the  corners  B  and  C  over  the  pulleys 
M  and  N.  Weights  P  and  P'  are  attached  to  the  ends  of  these 
cords.  The  number  of  ounces  in  the  weight  P  is  equal  to  the 
number  of  inches  in  the  side  A  B;  and  the  number  of  ounces 
in  /",  to  the  number  of  inches  in  A  C.  Hang  from  A  a  weight 
P"  less  than  the  sum  of  P  and  P' .  The  parallelogram  will  take 
up  a  position  of  equilibrium  such  that  the  cords  attached  to  B 
and  C  will  be  found  to  form  prolongations  of  the  sides  A  B  and 


NATURAL    PHILOSOPHY. 


A  C,  and  the  diagonal  A  D  will  be  vertical.  The  number  of 
inches  in  the  diagonal  will  be  found  to  be  equal  to  the  flumber 
of  ounces  in  the  weight  hung  from  A.  The  two  forces  P  and 
P'  which  are  acting  on  the  point  A  are  represented  by  the  lines 
A  B  and  A  C,  and  their  resultant  by  the  diagonal  A  D.  This 
vertical  resultant  is  balanced  by  the  equal  force  P"  acting  in  the 
opposite  direction. 


46.  Composition  of  Several  Oblique  Forces  acting  upon  a 
Point.—  When  several  forces  A  B,  A  C,  A  D,  and  A  E  (Fig- 
ure 12)  are  acting  upon  a  point  A,  their  resultant  may  be  found 
by  the  following  method  :  - 

Fig.  13. 


First  find  the  resultant  A  R1  of  the  two  forces  A  B  and  A  C\ 
then  the  resultant  A  A*2  of  the  first  resultant  A  Rl  and  of  the 
third  force  AD;  and,  finally,  the  resultant  A  R*  of  the  second 
resultant  A  Rl  and  of  the  fourth  force  A  E.  This  last  resultant 
will  be  the  resultant  of  all  the  forces. 


32  NATURAL    PHILOSOPHY. 

47.  Composition  of  two  Parallel  Forces  acting  in  the  Same 
Direction  on  Different  Points.  —  Suppose  two  parallel  forces 
A  B  and  CD  (Figure  13)  acting  in  the  same  direction  on  points 
at  the  extremities  of  the  line  A  C.  Their  resultant  PR  will 
have  an  intensity  equal  to  the  sum  of  the  intensities  of  the  two 
components,  a  direction  the  same  as  that  of  the  components, 
and  a  point  of  application  P  in  the  line  A  C  at  distances  from 
A  and  C  inversely  proportional  to  the  intensities  of  the  forces 
acting  on  those  points.  That  is  to  say,  PA:PC=  CD  :  A  B. 
Fig.  14. 


This  fact  may  be  verified  by  experiment  as  shown  in  Figure 
14.  A  straight  bar  is  suspended  at  its  centre  O  by  a  cord  which 
passes  up  over  the  pulley  above.  A  weight  is  attached  to  the 
end  of  the  cord  just  sufficient  to  balance  the  bar.  If  now  two 
weights  are  hung  from  the  arms  of  the  bar,  it  will  be  found  that 
they  will  be  balanced  by  a  weight  equal  to  their  sum  hung  upon 
the  end  of  the  cord,  provided  the  distances  from  O  to  the  points 
of  suspension  of  the  weights  on  the  arms  are  in  the  inverse  ratio 
of  the  weights.  In  the  first  case  shown  in  the  figure,  the  weights 
suspended  at  A  and  Z?are  equal,  and  also  the  distances  O  A  and 
OB.  In  the  second  case,  the  weight  at  Cis  double  that  at  B, 
and  the  distance  O  C  is  one  half  that  of  OB.  The  force  which 
balances  the  two  forces  on  the  arms  must  have  the  same  inten- 


NATURAL    PHILOSOPHY. 


33 


1 


sity  and  point  of  application  as  the  resultant  of  these  forces,  but 
the  opposite  direction. 

48.  Composition  of  two  Parallel  Forces  acting  in  Opposite 
Directions  on  Different  Points.  —  Suppose  two  parallel  forces 
A  B  and  CD  (Figure  15)  to  act  in  Fig.  15. 

opposite  directions  on  the  points  A 
and  C.    Their  resultant  P  A  will  have 
an  intensity  equal  to  the  difference  of 
intensities  of  the  two  components,  the 
direction  of  the  larger  component,  and 
a  point  of  application  P  in  the  same 
line  as  A  and  C,  and  at  distances  from 
A  and  C  inversely  proportioned  to  the    B 
intensities  of  the  forces  applied  at  those  points.     That  is  to  say, 
PA  :  PC=  CD  :  A  B. 

The  more  nearly  equal  the  two  forces  A  B  and  CD,  the  less 
the  intensity  of  their  resultant  and  the  more  distant  its  point  of 
application.  When  these  two  forces  are  equal  they  have  no 
resultant.  This  peculiar  system  of  parallel  forces  is  called  a 
couple.  There  is  no  force  that  will  balance  it.  It  does  not  tend 
to  produce  any  motion  of  translation,  but  one  of  rotation. 

49.  Composition  of  Several  Parallel  Forces  acting  upon 
Different  Points.  —  To  find  the  resultant  of  several  parallel 

Fig.  16.  Fig.  17. 


fttfi 


forces  A  F,  B  F>,  CF",  D  F'"  (Figure  16)  acting  upon  the  points 
A,  B,  C,  D,  first  find  the  resultant  Sroi  A  FandBF*,  then  the 
resultant  K  r1  of  Ir  and  C  F",  and,  finally,  the  resultant  L  R  of 
fCr1  and  D  F'".  This  last  resultant  will  be  the  resultant  of  all 
the  forces. 


34  NATURAL   PHILOSOPHY. 

50.  Resolution  of  a  Force  into  two  Oblique  Forces  with  the 
Same  Point  of  Application.  —  To  resolve  the  force  A  R  (Figure 
17)  into  two  oblique  forces  having  the  directions  of  A  B  and 
A  C,  draw  R  M  parallel  to  A  C  and  R  N  parallel  to  A  B.     AN 
and  A  M  will  represent  the  forces  required. 

51.  Resolution  of  the  Force  of  the   Wind  in  the   Case  of  a 
Sailing  Vessel.  —  Let  the  line  AB  (Figure    18)  represent  the 
direction  of  the  keel  of  the  vessel ;    the  line  CD,  the  direction 
of  the  face  of  the  sail ;  and  the  line   WE,  the  direction  and  in- 
tensity of  the  wind.     To  find  the  intensity  of  the   force  which 
would  be  effective  in  driving  the  vessel  forward,  first  decompose 
the   force  of  the  wind   WE  into  two   components,  one  D  E 

Fig.  18.  tangent  to  the  sail,  and  the  other 

dv  F  E  perpendicular   to   the    sail. 

^    >^  This  later  component  will  be  the 

~B  only  part  of  the  force  of  the  wind 
that  will  have  any  effect  upon  the 
sail.  This  force  must  again  be 


' D  decomposed  into  two  components, 
one  GE  perpendicular  to  the 
length  of  the  vessel,  and  the  other 
HE'vci  the  direction  of  the  vessel.  This  last  component  will 
be  the  only  portion  of  the  force  of  the  wind  that  will  be  effec- 
tive in  moving  the  vessel  forward. 

D.   GRAVITY  AND  EQUILIBRIUM. 

52.  Law  of  Gravity.  —  The   law  of   gravity   was   dis- 
covered by  Newton.    It  is  as  follows  :  Every  portion  of  mat- 
ter attracts  every  other  portion  of  matter  with  a  force  directly 
proportional  to  the  product  of  the  masses  acted  upon,  and  in- 
versely proportional  to  the  square  of  the  distances  betiveen  them. 

53.  Centre  of  Gravity.  —  The   direction  of  gravity  at   the 
surface  of  the  earth  is  that  of  a  plumb  line.     Gravity  acts  upon 
each  particle  of  which  a  body  is  composed,  and  the  forces  of 
gravity  acting  upon  the  various  particles  of  a  body  are  parallel 
forces.      The  point   of  application  of  the   resultant  of   these 
various  parallel  forces  is  called  the   centre  of  gravity   of  the 
body.    Thus,  G  is  the  centre  of  gravity  of  the  stone  in  Fig- 


NATURAL    PHILOSOPHY. 


35 


ure  19.    The  whole  of  the  force  of  gravity  acting  upon  a  body 

may  be   considered  as  applied  at  the  centre  of  gravity.     If  a 

force  equal  to  the  resultant  of  the 

forces  of  gravity  be  applied  to  the 

centre  of  gravity  in  the  opposite 

direction,  the  body  will  balance 

or  be  in  equilibrium. 

The  centre  of  gravity  may 
be  defined  as  the  point  upon 
which  the  body  will  balance  in 
every  position.  When  a  body 
is  homogeneous  throughout, 
the  centre  of  gravity  is  at  the 
centre  of  figure  of  the  body. 
When  the  body  is  not  homo- 
geneous throughout,  the  centre 
of  gravity  is  away  from  the  centre  of  figure  towards  the 
denser  side  of  the  body.  The  centre  of  gravity  often  lies 
entirely  outside  of  the  material  of  the  body,  as  in  the  case 
of  a  ring  or  a  hollow  sphere.  When  this  is  the  case,  the 
centre  of  gravity  must  be  rigidly  connected  to  the  body  in 
order  to  have  the  body  balance  on  it.  A  system  of  bodies 
may  have  a  common  centre  of  gravity  lying  outside  of  all 
the  bodies.  The  centre  of  gravity  of  two  spheres  will  lie 
somewhere  on  a  line  between  the  centres  of  gravity  of  the 
spheres  themselves.  If  the  spheres  have  the  same  mass, 
this  point  will  lie  just  midway  between  their  centres  of 
gravity.  If  one  sphere  has  a  greater  mass  than  the  other, 
the  centre  of  gravity  of  the  system  will  lie  nearer  the  cen- 
tre of  gravity  of  the  larger  sphere.  If  there  is  sufficient 
difference  between  the  masses  of  the  spheres,  their  com- 
mon centre  of  gravity  may  lie  within  the  larger  sphere. 

54.  Experimental  Method  of  finding  the  Centre  of  Grav- 
ity.—  Since  the  resultant  of  the  forces  of  gravity  acting 
upon  a  body  and  the  force  which  balances  it  must  act 


36 


NATURAL   PHILOSOPHY. 


along  the  same  line   in  opposite  directions,  if  a  body  be 
suspended  so  as  to  turn  freely,  its  centre  of  gravity  must 

be  in  a  vertical  line 
under  the  point  of  sus- 
pension. Hence,  if  we 
suspend  any  body  from 
two  points  and  mark  the 
vertical  lines  from  each 
point  of  suspension,  the 
centre  of  gravity  must 
be  where  these  verticals 
cross  (Figure  20). 

55.  Kinds  of  Equilibrium.  —  When   a  body,  on    being 
tipped  a  little,  tends  to  return  to  its  old  position,  it  is  said 
to  be  in  stable  equilibrium  ;  when  it  tends  to  fall  to  a  new 
position,  in  unstable  equilibrium  ;  and  when  it  rests  equally 
well  in  every  position,  in  indifferent  equilibrium. 

When  a  body  is  in  stable  equilibrium,  its  centre  of 
gravity  rises  on  tipping  the  body ;  when  it  is  in  unstable 
equilibrium,  its  centre  of  gravity /#//.$•  on  tipping  the  body ; 
and  when  it  is  in  indifferent  equilibrium,  its  centre  of 
gravity  neither  rises  nor  falls  on  tipping  the  body. 

56.  Equilibrium  of  a  Body  resting  on  a  Fixed  Point  or 
Axis.  —  A  body  resting  on  a  point  or  axis  can  be  in  equi- 


Fig.  21. 


Fig.  22. 


NATURAL   PHILOSOPHY.  37 

librium  only  when  the  centre  of  gravity  and  the  point  or 
axis  of  support  lie  in  the  same  vertical  line.  This  can 
be  the  case  only  when  the  centre  of  gravity  is  either 
directly  above  or  below  the  point  or  axis  of  support.  In 
the  former  case  the  body  is  in  unstable  equilibrium.  This 
case  is  shown  in  Figure  21.  O  is  the  axis  of  support,  and 
G  the  centre  of  gravity.  It  will  be  seen  that  gravity  will 
tend  to  topple  the  body  over  as  soon  as  it  is  tipped.  In 
the  latter  case  the  body  is  in  stable  Fig.  23. 

equilibrium.  This  case  is  shown 
in  Figure  22.  As  soon  as  the 
body  is  tipped  gravity  tends  to 
right  it. 

The  toy  called  the  balancer  (Fig- 
ure 23)  is  an  illustration  of  stable 
equilibrium  of  a  body  resting  on  a 
point.  The  balls  at  the  ends  of  the 
wires  at  each  side  of  the  figure 
bring  the  centre  of  gravity  of  the 
whole  below  the  toe  on  which  the 
Fig.  24.  '  figure  is  resting. 

In   a  similar  way 
a  cork  may  be  bal- 
anced on  the  point  of  a  needle  by  sticking 
two  forks  into  it,  as  shown  in  Figure  24. 

When -the  centre  of  gravity  is  at  the  point 
or  axis  of  support,  the  body  is  in  indifferent 
equilibrium. 

57.  Equilibrium  of  a  Body  resting  on  a  Horizontal  Plane 
at  One  Point  only.  —  Such  a  body  can  be  in  equilibrium 
only  when  its  centre  of  gravity  and  the  point  where  it 
touches  the  plane  are  both  in  the  same  vertical.  Figure 
25  represents  two  positions  of  equilibrium  of  an  oval  body 
on  a  horizontal  plane.  In  the  first  case  the  body  is  in 
unstable  equilibrium,  because  its  centre  of  gravity  will 


56202 


38  ,  NATURAL    PHILOSOPHY. 

begin  to  fall  as  soon  as  it  is  tipped.  In  the  second  case 
the  body  is  in  stable  equilibrium,  because  its  centre  of 
gravity  is  in  its  lowest  possible  position. 

Fig.  25. 


The  toy  called  the  tumbler  is  an  illustration  of  stable 
equilibrium  of  a  body  touching  a  horizontal  plane  at  one 
point.  The  centre  of  gravity  is  so  low  down  that  the 
body  cannot  be  tipped  without  raising  this  point.  This 
toy  is  shown  in  Figure  26. 

Fig.  26. 


58.    Equilibrium  of  a  Body  resting  on  a  Horizontal  Plane 
at  Several  Points.  —  Such  a  body  will  be  in  stable  equilib- 
Fig  2?  rium  when  the  vertical  line 

from  its  centre  of  gravity 
passes  within  the  polygon 
formed  by  joining  the  sev- 
eral points  on  which  the 
body  rests  (Figure  27). 
This  polygon  is  called  the 
base  of  the  body.  The 
lower  the  centre  of  gravity, 


NATURAL    PHILOSOPHY. 


39 


and  the  greater  the  distance  of  its  vertical  from  the 
nearest  side  of  the  base,  the  greater  the  stability  of  the 
equilibrium  of  the  body,  because  the  farther  the  body 
would  have  to  be  tipped,  and  the  more  its  centre  of  grav- 
ity would  have  to  be  raised,  to  overturn  it  (Figure  28). 
For  this  reason  a  high  load  is  more  likely  to  tip  over  than 
a  low  one.  A  leaning  body  may  be  in  stable  equilibrium. 

Fig.  28. 

d_ 


*-  o 

5\  

........ 

\ 

X          S 

"\ 

59.  Weight.  —  Weight  is  the  downward  pressure  which 
gravity  causes  a  body  to  exert.  While  a  body  will  have 
the  same  mass  wherever  it  may  be,  its  weight  will  vary 
with  the  force  of  gravity  acting  upon  it.  At  twice  the 
distance  from  the  centre  of  the  earth,  a  body  would  have 
only  one  fourth  the  weight  it  has  at  the  surface  of  the  earth. 
On  the  sun  the  same  body  would  have  28  times  the  weight 
it  has  on  the  earth.  The  English  unit  of  weight  is  the 
pound  avoirdupois ;  the  French  unit  is  the  gramme. 

The  weight  of  a  body  is  ascertained  either  by  finding 
how  much  it  will  bend  a  spring,  as  in  the  spring  balance, 
or  by  finding  how  many  known  weights  at  one  end  of  a 
beam  will  counterpoise  it  when  placed  on  the  other  end, 
as  in  the  ordinary  balance.  By  the  last  method  the 
weight  of  the  body  would  be  found  to  be  the  same  every- 
where, for  it  is  not  the  weight  of  the  body  which  is  found 
in  this  case,  but  its  mass.  This  is  found  by  comparing 
the  weight  of  a  body  with  that  of  a  known  mass.  The 


4°  NATURAL    PHILOSOPHY. 

weight  of  the  mass  to  be  weighed,  and  that  of  the  mass  used 
to  counterpoise  it,  both  change  with  the  force  of  gravity. 

60.  The  Balance.  —  The  balance  (Figure  29)  consists  of 
a  rigid  bar  A  J3,  called  the  beam,  supported  on  an  axis  O 

Fig.  29.  at    its    centre.     This    axis 

rests  upon  two  plates,  and 
is  just  above  the  centre  of 
gravity  of  the  beam,  that 
the  beam  may  be  in  stable 
equilibrium.  An  index  point 
attached  to  the  beam  moves 
over  a  graduated  arc.  When 
the  index  points  to  zero,  the 
beam  is  in  equilibrium.  Two 
scale  pans,  of  the  same  ma- 
terial, form,  and  weight,  are  suspended  from  the  ends  of 
the  beam  at  equal  distances  from  the  axis  of  support. 
The  body  to  be  weighed  is  placed  in  one  of  these  pans, 
and  is  counterpoised  by  known  weights  in  the  other. 

61.  The  Correctness  of  the  Balance.  —  For  the  balance  to  give 
true  weights,  it  is  necessary  that  the  arms  of  the  beam  should 
be  of  exactly  the  same  length.     To  test  the  correctness  of  the 
balance,  reverse  the  position,  of  the  body  weighed  and  of  the 
weight.     If  the  balance  is  true,  the  index  will  still  point  to  zero. 

As  it  is  very  difficult  to  make  the  two  arms  of  exactly  the  same 
length,  the  method  of  double  -weighing  is  employed  whenever 
great  accuracy  is  required.  By  this  method  we  may  obtain 
exact  weight,  even  when  the  arms  are  slightly  unequal.  The 
body  to  be  weighed  is  first  counterpoised  with  any  convenient 
substance,  as  shot  or  sand.  It  is  then  removed,  and  the  shot 
or  sand  is  counterpoised  by  known  weights  in  place  of  the  body. 
These  will  give  the  exact  weight  of  the  body,  since  they  are 
counterpoised  by  exactly  the  same  thing  under  exactly  the  same 
circumstances. 

62.  The  Sensibility  of  the  Balance.  —  The  sensibility  of  the 
balance  depends  upon  the  ease  with  which  the  beam  is  tipped. 


NATURAL   PHILOSOPHY. 


4' 


The  less  the  difference  of  weight  in  the  two  pans  that  will  cause 
the  beam  to  incline,  the  more  sensitive  the  balance.  The  longer 
and  lighter  the  beam,  the  nearer  its  centre  of  gravity  to  the 
axis  of  support,  and  the  less  the  friction  of  this  axis  upon  its 
supports,  the  more  sensitive  the  balance.  In  carefully  con- 
structed balances,  to  make  the  friction  as  slight  as  possible,  the 
axis  is  formed  by  the  edge  of  a  triangular  piece  of  steel,  called 
the  knife-edge;  and  this  knife-edge  rests  upon  plates  of  very 
hard  steel  or  of  agate. 

63.  Specific  Gravity.  —  The  specific  gravity  of  a  sub- 
stance is  its  weight  compared  with  the  weight  of  the  same 
bulk  of  some  standard  substance.  The  substance  com- 
monly taken  as  the  standard  for  solids  and  liquids  is 
distilled  water  at  a  temperature  of  39°  F.  A  cubic  foot  of 
such  water  weighs  62.425  Ibs.  avoirdupois.  The  weight 
of  a  gallon  of  water  is  10  Ibs.  The  weight  of  a  cubic  cen- 
timetre of  water  is  a  gramme,  and  the  weight  of  a  litre  of 
water  is  a  kilogramme. 

In  the  following  table  we  give  the  specific  gravities  of  some 
liquids  and  solids. 

Liquids,  at  Temperature  of  Freezing  Water. 


Water,  sea,  ordinary 

.  1.026 
•  701 

Oil,  linseed 
"  olive 

.     .     .    .940 

•  QI  <* 

"        proof  spirit 

.Ql6 

"  whale  . 

•     -Q21 

Ether  

.     .716 

"  turpentine 

.   .   .  .870 

Mercury     .... 
Naphtha     . 

I3-S96 
.848 

Blood,  human  . 
Milk,  of  cow    . 

.  .   .  1.055 
.  .  .  1.03 

Solids. 


Brass,  cast .     .      7.8  to  8.4 

"      wire 8.54 

Bronze    8.4 

Copper,  cast    ....  8.6 

"        sheet .     .     .     .8.8 

"        hammered   .     .  8.9 

Gold  ....      19  to  19.6 

Iron,  cast    .     .    6.95  to  7.3 


Iron,  wrought .     .  7.6  to  7.8 

Lead 11.4 

Platinum     .     .     .     .  21  to  22 

Silver 10.5 

Steel  ...  7.8  to  7.9 
Tin  ....  7.3  to  7.5 
Zinc  ....  6  8  to  7.2 
Ice 92 


42  NATURAL    PHILOSOPHY. 


Basalt 3.00 

Brick        .     .     .     .     2  to  2.17 

Brickwork 1.8 

Chalk       .     .     .     .  1.8  to  2.8 

Clay 1.92 

Glass,  crown      .     .     .     .2.5 
"       flint 3.0 


Quartz  (rock  crystal)       .  2.65 

Sand         1.42 

Fir,  spruce         .     .    .48  to  .7 
Oak,  European       .    .69  to  .99 
Lignum-vitae      .       .65  to  1.33 
Sulphur,  octahedral    .     .  2.05 
"        prismatic      .     .  1.98 


The  weight  of  a  cubic  foot  of  any  substance  is  equal  to 
62.425  Ibs.  avoirdupois  multiplied  by  its  specific  gravity. 

The  weight  of  a  cubic  centimetre  of  any  substance,  in 
grammes,  is  equal  to  its  specific  gravity. 

The  weight  of  a  litre  (or  cubic  decimetre)  of  any  substance, 
in  kilogrammes,  is  equal  to  its  specific  gravity. 

The  weight  of  a  gallon  of  any  liquid,  in  Ibs.  avoirdupois,  is 
equal  to  its  specific  gravity  multiplied  by  10. 

QUESTIONS  ON   THE  A  BO  YE    TABLE. 

41.  What  is  the  weight  of  a  cubic  foot  of  mercury  ? 

42.  What  is  the  weight  of  a  gallon  of  milk  ? 

43.  How  many  gallons  in  50  Ibs.  of  pure  alcohol  ? 

44.  What  is  the  weight  of  15  litres  of  ether  ? 

45.  How  many  litres  in  8  kilogrammes  of  olive  oil  ? 

46.  What  is  the  weight  of  a  cubic  foot  of  bronze  ? 

47.  What  is  the  weight  of  a  cubic  yard  of  clay  ? 

48.  What  is  the  weight  of  a  cubic  foot  of  flint  glass  ? 

49.  What  is  the  weight  of  a  cubic  inch  of  silver  ? 

50.  How  many  cubic  feet  in  a  ton  of  ice  ? 

51.  How  many  cubic  inches  in  a  pound  of  quartz  ? 

52.  What  is  the  weight  of  a  cubic  decimetre  of  silver  ? 

53.  What  is  the  weight  of  a  cubic  metre  of  lead  ? 

54.  What  is  the  weight  of  a  cubic  kilometre  of  basalt  ? 

55.  How  many  cubic  centimetres  in  9  kilogrammes  of  cast 
copper  ? 

E.    FALLING  BODIES. 

64.  All  Bodies  fall  at  the  Same  Rate  in  a  Vacuum.  — 
That  light  and  heavy  bodies  fall  at  the  same  rate  in  a 
vacuum  may  be  shown  with  the  guinea  and  feather  tube 
(Figure  30).  The  tube  contains  a  bit  of  metal  and  a 


NATURAL    PHILOSOPHY. 


45 


feather.     Exhaust  the  air  from  the  tube,  and  invert  the 
tube.      The  metal  and   the  feather  will    be  seen    to  fall 


Fig.  30. 


through  the  tube  at  the  same  rate. 

The  reason  that  light  and  heavy 
bodies  fall  in  a  vacuum  at  the  same  rate 
is  that  the  force  of  gravity  acting  upon 
a  body  varies  directly  as  the  mass  of  the 
body.  The  force  of  gravity  on  a  mass 
of  a  pound  is  about  32  poundals  ;  on  a 
mass  of  two  pounds,  64  poundals  ;  on 
a  mass  of  half  a  pound,  16  poundals; 
on  a  mass  of  one  ounce,  2  poundals  ; 
etc.  The  force  of  gravity  on  a  mass  of 
one  gramme  is  about  981  dynes;  on  a 
mass  of  a  decagramme,  9810  dynes  ;  on 
a  mass  of  a  decigramme,  98.1  dynes; 
etc.  Since  the  intensity  of  the  gravity 
acting  upon  a  body  increases  just  as 
rapidly  as  the  mass  of  the  body,  gravity, 
if  left  to  itself,  would  cause  all  bodies 
to  fall  at  the  same  rate  ;  for  if  the  mass 
of  one  body  is  twice  or  thrice  as  great 
as  that  of  another,  gravity  will  act 
upon  it  with  twice  or  thrice  the  in- 
tensity. 

65.  Bodies  fall  with  Unequal  Velocities 
in  the  Air.  —  A  bullet  will  fall  through  the  air  much  faster 
than  a  feather.  The  air  offers  resistance  to  every  body 
falling  through  it.  The  denser  a  body  and  the  less  its 
surface,  the  less  its  motion  is  retarded  by  the  air.  Gold- 
leaf  falls  slowly  in  the  air,  while  the  same  gold  in  the  form 
of  a  solid  sphere  would  fall  almost  as  rapidly  in  the  air  as 
in  a  vacuum. 

The  resistance  of  the  air  increases  with  the  velocity,  and 
after  a  while  it  becomes  equal  to  the  attraction  of  gravity 


44  NATURAL   PHILOSOPHY. 

upon  a  body.  When  this  is  the  case,  the  body  will  gain  no 
more  velocity,  but  keep  falling  at  a  uniform  rate.  Were  a 
body  shot  downward  with  a  velocity  greater  than  this,  it 
would  be  retarded  by  the  resistance  of  the  air,  which  would 
then  be  greater  than  the  pull  of  gravity,  until  its  velocity 
were  reduced  to  that  at  which  the  resistance  of  the  air 
would  be  just  equal  to  the  pull  of  gravity. 

66.  Acceleration  produced   by   Gravity.  —  When  bodies 
are  falling  near  the  earth,  gravity  increases  their  velocity  at 
the  uniform  rate  of  about  32.2  feet  a  second,  in  a  vacuum. 
This  acceleration  per  second  produced  by  gravity  is  usually 
represented  by  g,  and  is  called  the  intensity  of  gravity.    It 
is  equal  to  about  981  centimetres,  or  9.81  metres.    When  a 
body  is  rising,  gravity  retards  its  velocity  at  the  rate  of  32.2 
feet,  or  9.81  metres  a  second.    Were  a  body  thrown  up  in  a 
vacuum,  it  would  be  just  as  many  seconds  in  falling  as  it  is 
in  rising,  and  it  would  reach  the  point  it  started  from  with 
the  velocity  it  had  on  starting.     It  gains  just  as  much 
velocity  in  falling  as  it  lost  in  rising. 

67.  Velocity  acquired  by  a  Body  falling  from   a   State  of 
Rest.  —The  velocity  acquired  by  a  body  falling  from  a  state  of 
rest  will  be  equal  to  the  product  of  the  intensity  of  gravity  by  the 
number  of  seconds  the  body  has  been  falling.     If  we  represent 
the  velocity  acquired  by  v,  and  the  number  of  seconds  the  body 
has  been  falling  by  /,  the  formula  for  the  velocity  of  a  body 
falling  from  a  state  of  rest  will  be  v  =  gt. 

If  a  body  were  falling  from  a  state  of  rest,  the  number  of  feet 
of  velocity  it  would  acquire  in  20  seconds  would  be  32.2  X 
20  =  644  ;  and  the  number  of  metres  of  velocity  it  would 
acquire  would  be  9.81  X  20  =  196.2. 

68.  Distance  passed  over  by  a  Body  falling  from  a  State  of 
Rest.  —  The  distance  passed  over  by  a  moving  body  is  always 
equal  to  the  product  of  its  mean  velocity  by  the  time.     Since 
falling  bodies  gain  velocity  at  a  uniform  rate,  the  mean  velocity 
of  a  body  falling  from   a   state  of  rest  will   be  one  half   the 
velocity  it  has  acquired.     We  saw,  in  the  last  section,  that  the 


NATURAL    PHILOSOPHY.  45 

velocity  acquired  at  any  time  was  gt.  Hence  the  mean  velocity 
will  be  l/2  gt.  If  we  represent  the  distance  passed  over  by  s, 
we  shall  have 


The  distance  passed  over  by  a  body  falling  4  seconds  from 
a  state  of  rest  would  be  equal  to  16.1  X  16  =  257.6  feet,  or  to 
4.9  X  i6=78.4metres- 

69.    Formula  for  Falling  Bodies.  — 

From  the  formula 

v=gt  (a) 

we  have 

t  =  "-.  (b) 

g 

Substituting  this  value  of  /  in  the  formula 

s  =  \gt\  (c) 

we  have 

/-*.  (4 


(f) 
Also,  by  transposing  the  formula 

*  =  $£?, 
we  have 

f=^ 

and 


How  long  would  it  take  a  body  falling  from  a  state  of  rest  to 
acquire  a  velocity  of  193.2  feet  ? 


How  long  would  it  take  a  body  falling  from  a  state  of  rest  to 
acquire  a  velocity  of  39.24  metres  a  second  ? 


v  . 

/  =  -  =  2r±±  —  4  seconds. 
g        9.81 


46  NATURAL   PHILOSOPHY. 

How  far  must  a  body  fall  from  a  state  of  rest  to  acquire  a 
velocity  of  1500  feet  a  second? 

7/2  225OOOO 

s  =  —  •  =  —         —  =  34938  feet. 

2g  64.4 

How  far  must  a  body  fall  from  a  state  of  rest  to  acquire  a 
velocity  of  800  metres  a  second  ? 

vz        640000 

s  =  —  =  -  -;  —  =  32619.7  metres. 
2g         19.62 

How  long  would  it  take  a  body  to  fall  750  feet  from  a  state  of 
rest,  and  what  velocity  would  it  acquire  ? 


=  J—  = 

V 


=  6.8  seconds. 


g         32.2 


v  =  \J2gs  =  ^64.4  X  750  =  219.8  feet. 

QUESTIONS  ON  FALLING   BODIES. 

56.  How  many  feet  of  velocity  would  a  body  acquire  in  falling 
25  seconds  from  a  state  of  rest  ? 

57.  How  many  metres  of  velocity  would  a  body  acquire  in 
falling  42  seconds  from  a  state  of  rest  ? 

58.  How  long  would  a  body  have  to  fall  from  a  state  of  rest 
to  acquire  a  velocity  of  986  feet  ? 

59.  How  long  would  a  body  have  to  fall  from  a  state  of  rest 
to  acquire  a  velocity  of  25,000  centimetres  a  second  ? 

60.  How  many  feet  would  a  body  fall  from  a  state  of  rest  in 
32  seconds  ? 

61.  How  many  metres  would  a  body  fall  from  a  state  of  rest 
in  45  seconds  ? 

62.  How  far  would  a  body  have  to  fall  from  a  state  of  rest  to 
acquire  a  velocity  of  1200  feet  a  second  ? 

63.  How  far  would  a  body  have  to  fall  from  a  state  of  rest  to 
acquire  a  velocity  of  300  metres  a  second  ? 

64.  What  velocity  would  a  body  acquire  in  falling  600  feet 
from  a  state  of  rest  ? 

65.  What  velocity  would  a  body  acquire  in  falling  900  metres 
from  a  state  of  rest  ? 


NATURAL   PHILOSOPHY.  47 

66.  How  long  would  it  take  a  body  to  fall  700  feet  from  a 
state  of  rest  ? 

67.  How  long  would  it  take  a  body  to  fall  500  metres  from  a 
state  of  rest  ? 

70.  Height  to  which  a  Body  can  rise.  —  A  body  moving 
upward  will  continue  to  rise  till  all  of  its  velocity  is  exhausted. 
A  rising  body  loses  velocity  just  as  fast  as  a  falling  body  gains 
it.  Hence  the  height  to  which  a  body  can  'rise  with  a  given 
velocity  is  just  equal  to  the  height  from  which  it  must  fall  to 
gain  that  velocity.  The  height  to  which  a  body  can  rise  will 
therefore  be  represented  by  the  formula 


In  this  case  s  is  the  distance  a  body  can  rise,  and  -v  the 
velocity  with  which  it  starts.  The  height  to  which  a  body  can 
rise  increases  as  the  square  of  the  velocity  with  which  it  starts. 

68.  How  high  could  a  body  rise,  starting  with  a  velocity  of 
250  feet  a  second  ?     Of  500  feet  a  second  ? 

69.  How  high  could  a  body  rise,  starting  with  a  velocity  of 
150  metres  a  second  ?     Of  300  metres  a  second  ? 

71.  Transformation  of  Energy  in  the  Case  of  a  Body 
Projected  upward.  —  When  a  body  is  projected  upward, 
its  energy  on  leaving  the  surface  of  the  earth  is  entirely 
kinetic.  As  it  rises,  it  moves  slower  and  slower,  and  so 
loses  kinetic  energy,  but  as  it  is  separated  farther  and 
farther  from  the  earth,  it  gains  potential  energy.  At  the 
highest  point  the  body  reaches,  its  energy  is  entirely  poten- 
tial. As  it  falls  -again,  it  moves  faster  and  faster,  and  so 
gains  kinetic  energy,  but  as  it  comes  nearer  and  nearer  the 
earth,  it  loses  potential  energy.  While  the  body  is  rising 
its  kinetic  energy  is  gradually  transformed  into  potential 
energy  ;  and  when  it  falls  again,  its  potential  energy  is 
changed  back  again  into  kinetic  energy.  The  energy 
possessed  by  the  body  is  precisely  the  same  at  every 
point  in  its  path.  When  the  body  strikes  the  earth,  its 
energy  is  apparently  destroyed  ;  but  when  we  come  to 


48  NATURAL    PHILOSOPHY. 

the  subject  of  Heat,  we  shall  see  that  this  is  not  really 
the  case. 

72.  The    Path    of   a    Body    Projected   horizontally    or 
obliquely.  —  When    a   body   is   projected    horizontally   or 
obliquely,  gravity  draws   it  towards  the  earth  faster   and 
faster  the  longer  it  acts  upon  it,  and  so  causes  it  to  de- 
scribe a  curved  path.     The  curve  in  this  case  would  be  a 
parabola  were  it  not  for  the  resistance  of  the  air. 

The  curved  line  in  Figure  31  shows  approximately  the 
path  of  a  cannon-ball  through  the  air,  when  fired  in  the 
Fig.  3..  direction  of  AB.   The 

line  A  C  represents 
the  range  of  the  ball,  or 
the  greatest  horizontal 
distance  it  is  thrown. 
Were  it  not  for  the 
resistance  of  the  air,  the  range  would  be  greatest  when 
the  cannon  was  pointed  45°  above  the  horizon. 

73.  Intensity   of    Gravity.  —  The   intensity   of    gravity 
varies  somewhat  as  we  pass  from  the  equator  to  the  poles. 
At  the  equator  its  intensity  is  sufficient  to  give  a  mass  in 
a  vacuum  an  acceleration  of  32.088  feet  per  second,  while 
at  the  poles  it  is  sufficient  to  give  a  mass  in  a  vacuum  an 
acceleration  of  32.253  feet  per  second.     The  value  of  g  in 
centimetres  varies  from  978.10  at  the  equator  to  983.11   at 
the  poles.     The  intensity  of  gravity  also  varies  with  the 
height.      At  twice  the  distance  from  the  centre  of   the 
earth,  the  intensity  of  gravity  is  only  one  fourth  as  great  as 
at  the  surface  of  the  earth. 

Since  a  poundal  is  a  force  that  will  give  to  a  mass  of  a 
pound  an  acceleration  of  a  foot  in  a  second,  and  since 
gravity  will  give  a  mass  of  a  pound  an  acceleration  of 
32.2  feet  a  second,  it  follows  that  there  are  about  32.2 
poundals  in  a  pound  at  Greenwich,  as  has  already  been 
stated.  A  poundal  is  about  half  an  ounce.  The  number 


NATURAL    PHILOSOPHY.  49 

of  poundals  in  a  pound  at  any  place  is  equal  to  the  value 
of  g  in  feet  at  that  place. 

Since  gravity  will  give  a  mass  of  a  gramme  an  accelera- 
tion of  981  centimetres,  it  follows  that  there  are  981  dynes 
in  a  gramme  of  force  at  Greenwich.  The  number  of 
dynes  in  a  gramme  at  any  place  is  equal  to  the  value  of  g 
in  centimetres  at  that  place. 

The  value  of  g  at  any  place  is  ascertained  by  means  of 
a  pendulum. 

F.  THE  PENDULUM. 

74.  The  Pendulum.  —  Any  body  free  to  turn  on  a  hori- 
zontal axis  which   does  not   pass  through  its   centre  of 
gravity  can  be  in  stable  equilibrium  only  when  its  centre 
of  gravity  is  below  the  axis  of  support  and  in       Fig.  32. 
the  same  vertical  plane  with  it.     When  pulled 

aside  from  this  position  of  equilibrium  and  re- 
leased, the  body  will  vibrate  back  and  forth 
across  its  position  of  stable  equilibrium,  until 
friction  and  the  resistance  of  the  air  bring  it 
to  rest.  A  body  suspended  in  this  way,  no 
matter  what  its  shape,  is  called  a  pendulum. 
The  usual  form  of  the  pendulum  is  that  shown 
in  Figure  32.  It  consists  of  a  rod  which  can 
turn  on  an  axis  O  at  its  upper  end,  and  which 
carries  a  heavy  lens-shaped  piece  of  metal  M, 
called  the  ball,  at  its  lower  end.  The  ball  can 
be  raised  or  lowered  by  means  of  the  screw  V. 

75.  The  Simple  Pendulum.  —  The   simple  pen- 
dulum is  an  ideal  pendulum  whose  ball  M1  (Figure 
33)  consists  of  a  single  heavy  particle   attached  to 
one  end  of  a  thread  of  invariable  length  and  without 
appreciable  mass,  which  is  fastened  at  the  other  end 
to  a  fixed  point  A.    When  the  thread  is  vertical,  the 
pull  of  gravity  upon  the  particle  is  in  the  direction 

of  the  thread,  and  hence  it  does  not  tend  to  move  the  particle  to 


50  NATURAL   PHILOSOPHY. 

the  right  or  to  the  left.     If  the  particle  is  drawn  aside  to  Af, 
Fig.  33.  the  pull  of  gravity  MG  upon  it  will  be  re- 

solved into  two  components  :  M  C  in  the 
direction  of  the  thread,  and  M  H  at  right 
angles  to  this  direction.  The  first  compo- 
nent will  be  balanced  by  the  resistance  of 
the  thread,  and  the  second  will  draw  the 
particle  to  the  right.  As  M  approaches  M', 
the  component  M  C  grows  larger  and 
larger,  and  the  component  M  //  smaller  and 
smaller,  vanishing  entirely  at  M'.  The 
kinetic  energy  which  the  particle  has  acquired 
in  passing  from  M  to  M'  will  carry  it  up  on  the  other  side.  The 
pull  of  gravity  will  again  be  resolved  into  two  components  after 
the  particle  passes  M',  and  the  component  M"  H"  will  now  tend 
to  stop  the  particle.  This  component  will  become  greater  and 
greater,  and,  if  there  were  no  external  resistance,  would  finally 
stop  the  particle  at  M",  just  as  far  to  the  right  of  M'  as  M  was 
to  the  left  of  it.  The  partfcle  will  then  return  to  M'  and  rise  to 
M  again,  and  so  on  indefinitely. 

The  arc  MM'  is  called  the  amplitude  of  the  vibration,  and 
the  time  the  particle  is  going  from  Afto  M"  is  called  the  time  of 
vibration.^ 

It  has  been  found,  by  mathematical  investigation,  that 
for  small  vibrations  the  time  of  vibration  is  independent  of  the 
amplitude ;  also,  that  the  time  of  vibration  increases  as  the 
square  root  of  the  length  of  the  pendulum,  and  decreases  as 
the  square  root  of  the  intensity  of  gravity  increases.  In  other 
words,  when  the  amplitude  does  not  exceed  3°  or  4°,  the 
same  pendulum  will  vibrate  at  the  same  rate,  no  matter 
what  may  be  the  amplitude  of  vibration  ;  but  if  the  pendu- 
lum is  made  four,  nine,  or  sixteen  times  as  long,  it  will 
vibrate  one  half,  one  third,  or  one  fourth  as  fast :  while,  if 
a  pendulum  were  kept  of  the  same  length,  and  the  intensity 
of  gravity  were  to  become  four,  nine,  or  sixteen  times  as 
great,  the  pendulum  would  vibrate  two,  three,  or  four  times 
as  fast. 


NATURAL    PHILOSOPHY.  5! 

76.  The  Formula  of  the  Pendulum.  —  Let  T  denote  the  time 
of  vibration,  /  the  length  of  the  pendulum,^  the  intensity  of 
gravity,  and  n  the  ratio  of  the  circumference  of  a  circle  to  its 
diameter,  then  the  formula  for  the  time  of  vibration  will  be 

T  = 
Squaring  both  sides,  we  have 

~~~g" 

Clearing  of  fractions,  we  have 

g  T-  =  TT*  /, 
and  dividing  by  Z2, 

g  =  ^-  .  0) 

If  we  could  construct  a  simple  pendulum,  all  that  we  should 
have  to  do  to  find  the  intensity  of  gravity  at  a  place  would  be  to 
measure  the  length  of  the  pendulum  and  count  its  rate  of  vibra- 
tion. Unfortunately  such  a  pendulum  has  only  an  ideal  existence, 
though  we  may  approximate  sufficiently  near  to  it  for  ordinary 
illustration  by  hanging  a  bullet  of  lead  on  a  fine  silk  thread. 

77.  The  Compound  Pendulum.  —  Every  pendulum  act- 
ually used  is  a  compound  pendulum,  consisting  of  a  heavy 
weight  hung  from  a  fixed  point  by  means  of  a  rod  of  wood 
or   metal.     Each  particle  of    such   a   pendulum   may  be 
regarded  as  a  simple  pendulum  ;  but  as  these  particles  are 
at  different  distances  from  the  point  of  suspension,  they 
tend  to  vibrate  at  different  rates.     The  particles  near  the 
point  of  suspension  are  retarded  by  the  tendency  of  the 
particles  below  them  to  vibrate   at  a  slower  rate,  while 
the  particles  near  the   lower  end   of   the  pendulum    are 
accelerated  by  the  tendency  of  the  particles  above  them 
to  vibrate  more  rapidly.     At  some   point  between   these 
there  must  be  a  particle  whose  vibration  is  neither  retarded 
nor  accelerated.     As  this  particle  is  vibrating  at  its  normal 
rate,  the  distance  of  this  particle  from  the  point  of  suspen- 
sion must  be  the  length  of  a  simple  pendulum  that  would 


52 


NATURAL    PHILOSOPHY. 


vibrate  at  the  rate  of  the  compound  pendulum.  The  point 
where  this  particle  is  situated  is  called  the  centre  of  vibra- 
tion; and  its  distance  from  the  point  of  suspension,  the 
virtual  length  of  the  pendulum. 

If  a  pendulum  is  inverted  and  suspended  by  its  centre 
of  vibration,  the  former  point  of  suspension  becomes  its 
new  centre  of  vibration.  This  remarkable  property  of  a 
compound  pendulum  enables  us  readily  to  find  the  centre 
of  vibration.  We  have  only  to  reverse  the  pendulum,  and 
find,  by  trial,  the  point  at  which  it  must  be  suspended  to 
vibrate  at  the  same  rate  as  before.  A  pendulum  con- 
structed for  this  purpose  is  called  a  reversible  pendulum. 


Fig.  34- 


78.  Use  of  the  Pendulum  for  meas- 
uring Time.  — The  most  important  use  of 
the  pendulum  is  for  measuring  time.  A 
common  clock  is  an  instrument  for  keep- 
ing a  pendulum  in  vibration,  and  record- 
ing its  beats.  The  essential  parts  of  the 
arrangement  by  which  this  is  accom- 
plished are  shown  in  Figure  34.  The 
scape-wheel  R  is  turned  by  a  weight  or 
spring,  and  its  motion  is  regulated  by 
means  of  the  escapement  m  n.  This 
turns  on  the  axis  <?,  and  is  connected 
with  the  pendulum  rod  by  means  of  the 
forked  arm  a  b.  When  the  pendulum  is 
at  rest,  the  hooks  n  and  m  of  the  escape- 
ment catch  the  teeth  of  the  scape-wheel, 
and  keep  it  from  turning.  As  the  pen- 
dulum vibrates,  the  hooks  of  the  escape- 
ment alternately  release  and  catch  the 
teeth  of  the  scape-wheel,  and  so  compel 
it  to  turn  slowly,  and  at  a  uniform  rate. 
The  hooks  of  the  escapement  are  of 
such  shape  that  each  tooth  of  the  scape- 


NATURAL    PHILOSOPHY.  53 

wheel,  as  it  slips  off  the  hook,  gives  the  escapement  a  littfe 
push  so  as  to  keep  up  the  vibration  of  the  pendulum. 

Each  tooth  of  the  scape-wheel  is  caught  twice  during  the 
revolution  of  the  wheel,  once  by  each  hook  of  the  escape- 
ment. Hence,  if  the  scape-wheel  has  thirty  teeth,  it  will 
make  one  revolution  for  every  sixty  beats  of  the  pendulum. 
The  axis  of  the  scape-wheel  carries  the  second-hand  of  the 
clock,  which  registers  the  beats  of  the  pendulum  up  to  sixty. 
The  scape-wheel  is  connected  with  another  which  turns  Jy 
as  fast.  The  axis  of  this  wheel  carries  the  minute-hand, 
which  registers  the  revolution  of  the  second-hand  up  to 
sixty.  This  second  wheel  is  connected  with  a  third  which 
turns  TV  as  fast  as  itself.  The  axis  of  this  last  wheel  car- 
ries the  hour-hand,  which  registers  the  revolution  of  the 
minute-hand  up  to  twelve,  or  half  a  day. 

79.  Transformations  of  Energy  in  the   Vibrations  of  the 
Pendulum.  —  When   the   pendulum    reaches    its    farthest 
point  to  the  right  or  left,  its  energy  is  entirely  potential ; 
and  when  its  ball  is  at  its  lowest  point,  its  energy  is  en- 
tirely kinetic.     As  the  ball  rises,  its  kinetic  energy  is  trans- 
formed  into   potential    energy,  and    as  it   falls  again,  its 
potential  energy  is  transformed  into  kinetic  energy. 

The  energy  consumed  in  overcoming  the  friction  of  the 
axis  of  the  pendulum  and  of  the  wheels  of  the  clock  and 
the  resistance  of  the  air  is  supplied  by  the  falling  weight  or 
uncoiling  spring;  and  when  the  store  of  energy  in  the 
weight  or  spring  is  consumed,  it  must  be  renewed  by  again 
raising  the  weight  or  coiling  the  spring  in  winding  up  the 
clock.  This  new  supply  of  energy  is  drawn  from  the  hand 
and  arm  of  the  person  who  winds  the  clock. 

G.  MACHINES. 

80.  Simple  Machines.  —  A  machine  is  an  instrument  by 
which  a  force  is  applied  to  do  work.     Every  machine,  how- 
ever complicated,  is  made  up  of  a  very  few  elements,  called 


34  NATURAL   PHILOSOPHY. 

simple  machines,  or  mechanical  powers.  These  are  the  lever, 
the  wheel  and  axle,  the  pulley,  the  inclined  plane,  the  wedge, 
and  the  screw. 

The  force  applied  to  work  the  machine  is  called  the 
power;  and  the  resistance  overcome  by  the  machine,  the 
work.  A  perfect  machine  would  be  one  which  offered  no 
friction  or  other  resistance  of  its  own.  Such  a  machine 
has  only  an  ideal  existence.  In  every  machine  in  actual 
use  the  work  done  is  partly  useful  in  overcoming  the 
resistance  we  desire  to  overcome,  and  partly  useless  in 
overcoming  the  resistance  of  the  machine  itself.  In  the 
theory  of  machines  the  resistance  of  the  machine  itself  is  left 
out  of  view.  The  magnitude  of  the  resistance  to  be  over- 
come is  represented  by  a  rising  weight,  and  the  magnitude 
of  the  power  is  usually  represented  by  a  falling  weight.  The 
resistance  to  be  overcome  is  technically  called  the  weight. 

81.  The  General  La-w  of  MacAines.  —  The  work  done  by 
the  power  upon  a  machine,  and  the  work  done  by  a  machine 
upon  the  resistance,  are  simply  different  aspects  of  the  same 
work,  and  hence  they  are  equal  in  amount.  Now  the  work 
done  by  a  falling  weight  is  equal  to  the  product  of  the 
weight  by  the  distance  it  falls,  and  the  work  done  in  raising 
a  weight  is  the  product  of  the  weight  by  the  distance  it  is 
raised.  If,  then,  we  represent  the  work  done  by  the  power 
upon  the  machine  by  a  falling  weight,  and  the  work  done 
by  the  machine  upon  the  resistance  by  a  rising  weight,  we 
arrive  at  the  following  general  principle  of  machines  :  The 
power  multiplied  by  the  distance  through  which  it  moves  is 
always  equal  to  the  weight  multiplied  by  the  distance  through 
which  it  moves.  This  is  simply  saying  that  the  work  done 
by  the  power  is  equal  to  the  work  done  upon  the  weight. 

The  following  facts  result  from  the  general  principle  of 
machines,  stated  above  :  — 

(i.)  The  faster  the  power  moves,  compared  with  the 
weight,  the  greater  the  weight  it  will  balance.  • 


NATURAL    PHILOSOPHY.  55 

(2.)  When  the  power  moves  faster  than  the  weight,  it 
will  balance  a  weight  greater  than  itself ;  and  when  it 
moves  slower  than  the  weight,  it  will  balance  a  weight  less 
than  itself  ;  and  when  it  moves  just  as  fast  as  the  weight, 
it  will  balance  a  weight  equal  to  itself. 

(3.)  The  power  will  balance  a  weight  just  as  many  times 
itself  as  it  moves  times  as  fast  as  the  weight. 

(4.)  In  any  machine,  the  power  and  weight  will  be  in  equi- 
librium when  they  are  in  the  inverse  ratio  of  their  velocities  ; 
that  is,  whichever  is  the  smaller  will  move  the  faster,  and 
just  as  many  times  as  fast  as  it  is  times  as  small.  The 
statement  in  italics  is  known  as  the  general  law  of  ma- 
chines. 

82.  Gain  and  Loss  of  Power  in  a  Machine.  — When,  in 
any  machine,  the  power  balances  a  weight  greater  than 
itself,  there  is  said  to  be  a  gain  of  power,  or  mechanical 
advantage ;  and  when  the  power  balances  a  weight  less  than 
itself,  a  loss  of  power,  or  mechanical  disadvantage. 

When  there  is  a  gain  of  power  there  is  always  a  cor- 
responding loss  of  speed,  and  when  there  is  a  loss' of  power 
there  is  a  corresponding  gain  of  speed. 

A  machine  might  be  described  as  an  instrument  by  which 
we  change  the  point  at  which  the  power  acts,  the  direction  in 
which  it  acts,  or  the  rate  at  which  it  acts.  The  last  change 
is  the  most  important  one  effected  by  a  machine.  When 
the  machine  causes  the  power  to  act  upon  the  resistance  at 
a  slower  rate  than  it  would  were  it  applied  directly  to  it, 
there  is  a  gain  of  power ;  and  when  it  causes  it  to  act  upon 
it  at  a  quicker  rate,  there  is  a  loss  of  power.  When  the 
machine  does  not  change  the  rate,  there  is  neither  gain  nor 
loss  of  power.  The  general  law  given  above  is  applied  to 
every  machine.  When  we  take  up  the  different  simple 
machines,  we  shall  give  the  special  law  of  each  ;  and  that 
is  the  law  which  concerns  the  relative  velocities  of  the 
power  and  weight. 


56  NATURAL    PHILOSOPHY. 

QUESTIONS  ON   THE   GENERAL   LAW  OF  MACHINES. 

70.  In  a  machine,  the  power  moves  25  inches  while  the  weight 
is  moving  35  inches.  What  weight  would  be  balanced  by  63 
pounds  of  power? 

If  we  denote  the  power  by  P,  the  weight  by  W,  the  velocity 
of  the  power  by  VP,  the  velocity  of  the  weight  by  V  W,  and  the 
distances  passed  over  by  the  power  and  weight,  respectively,  by 
D  P  and  D  W,  then  we  shall  have,  in  the  above  example, 
VP  —      VW 


W  =  45  pounds. 

71.  In  a  machine,  a  power  of  27  pounds  balances  a  weight  of 
45  pounds.     How  far  does  the  power  move  while  the  weight 
moves  60  inches  ? 

P  =  \  W 
.:   VP  =  \  VW 

DP  =  \  X  60=  100  inches. 

72.  In  a  machine,  the  power  moves  56  inches  while  the  weight 
moves  21  'inches?     What  power  will  balance  a  weight  of  600 
pounds  ? 

73.  In  a  machine,  the  power  moves  35  inches  while  the  weight 
is  moving  63  inches.      What  weight  will  be  balanced  by  250 
pounds  of  power? 

74.  In  a  machine,  the  power  moves  15  centimetres  while  the 
weight  moves  40  centimetres.    What  power  will  balance  a  weight 
of  90  grammes  ? 

75.  In  a  machine,  the  power  moves  24  centimetres  while  the 
weight  is  moving  56  centimetres.     What  weight  would  be  bal- 
anced by  130  grammes  of  power? 

76.  In  a  machine,  a  power  of  28  pounds  balances  a  weight  of 
49  pounds.    How  far  will  the  power  move  while  the  weight  moves 
20  inches? 

77.  In  a  machine,  a  power  of  40  pounds  balances  a  weight  of 
32  pounds  ?     How  far  will  the  weight  move  while  the  power  is 
moving  30  inches  ? 

78-    In  a  machine,  a  power  of  50  grammes  balances  a  weight 


NATURAL    PHILOSOPHY. 


57 


of  80  grammes.     How  far  will  the  power  move  while  the  weight 
is  moving  15  centimetres  ? 

79.  In  a  machine,  a  power  of  81  grammes  balances  a  weight 
of  63  grammes.  How  far  will  the  weight  move  while  the  power 
is  moving  25  centimetres  ? 

83.  The  Lever.  —  The  lever  is  a  rigid  bar,  capable  of  turn- 
ing upon  a  fixed  point  or  axis.  The  point  on  which  the 
lever  turns  is  called  the  fulcrum.  Fig.  35. 

Different  forms  of  the  lever  are 
shown  in  Figure  35.  F  is  the 
fulcrum,  IY  \\~\e  weight,  and  P  the 
power. 

When  the  fulcrum  is  between 
the  power  and  weight,  the  lever  is 
said  to  be  of  the  first  order ;  when 
the  weight  is  between  the  fulcrum 
and  power,  the  lever  is  said  to  be 
of  the  second  order;  and  when  the  power  is  between  the 
fulcrum  and  weight,  the  lever  is  said  to  be  of  the  third 
order. 


Fig.  36. 


Fig.  37- 


A  bar  used  for  raising  a  weight  is  a  lever.  When  it 
is  used  as  shown  in  Figure  36,  it  is  a  lever  of  the  first 
order.  When  it  is  used  as  shown  in  pig.  38. 

Figure  37,  it  is  a  lever  of  the  second 
order.  A  fishing-rod  (Figure  38)  is 
a  lever  of  the  third  order. 

The  arms  of  a  lever  are  the  distances  from  the  fulcrum  to 
the  points  where  the  power  and  weight  are  applied,  in  case 
the  lever  is  straight ;  or  the  distance  from  the  fulcrum  to  the 
lines  which  show  the  direction  of  the  power  and  weight,  in 
case  the  lever  is  bent. 


58  NATURAL   PHILOSOPHY. 

In  Figure  35,  FP  is  in  each  case  the  power  arm,  and 
Fig.  39.  F  W  tne  weight  arm.     In  Figure  39, 

the  dotted  lines,  which  are  supposed 
to  be  drawn  from  the  fulcrum  per- 
pendicularly to  the  directions  in 

which  the  weight  and  power  act,  are  the  arms  of  the  bent 
lever,  abfc. 

84.  The  Special  Law  of  the  Lever.  —  The  special  law  of 
the  lever  is,  that  the  velocities  of  the  power  and  weight  are 
in  the  direct  ratio  of  the  lengths  of  the  arms  to  which  they  are 
applied;  that  is,  if  one  arm  of  the  lever  be  three  times  as 
long  or  one-third  as  long  as  the  other,  the  power  or  weight 
applied  to  this  arm  will  move  three  times  as  fast  or  one 
third  as  fast  as  the  one  applied  to  the  other  arm. 

There  will  be  a  gain  of  power  in  the  lever  whenever  the 
power  arm  is  the  longer  ;  for  the  power  will  then  move  the 
faster,  and  will  balance  a  weight  greater  than  itself.  There 
will  be  a  loss  of  power  when  the  power  arm  is  the  shorter  ; 
for  the  power  will  then  move  the  slower,  and  will  balance 
a  weight  less  than  itself. 

In  a  lever  of  the  second  order  there  will  always  be  a  gain 
of  power,  and  in  a  lever  of  the  third  order  a  loss  of  power. 
In  the  lever  of  the  first  order  there  will  be  a  gain  or  loss  of 
power,  or  neither,  according"  as  the  fulcrum  is  nearer  the 
weight,  or  nearer  the  power,  or  midway  between  the  two. 

85.  The  Compound  Lever.  —  Sometimes  two  or  more  sim- 

Fig.  40.  pie  levers  are  combined,   as 

shown  in  Figure  40.  Suppose 
that  P  be  five  times  as  far 
from  the  fulcrum  /  as  A  is, 
the  point  P  will  then  move 
five  times  as  fast  as  the  point 
A,  and  a  pull  of  one  pound 
on  P  will  exert  a  pull  of  five  pounds  on  A.  If  B  is  five 
times  as  far  from  the  fulcrum  -Fas  W\^  the  five  pounds  of 


NATURAL   PHILOSOPHY.  59 

pull  on  B  will  exert  twenty-five  pounds  of  pull  at  W.  In 
this  case  one  pound  of  pull  exerted  at  P  will  balance 
twenty-five  pounds  at  W;  but  it  would  be  found  on  trial 
that  by  pulling  /Mown  one  inch,  W  would  be  raised  only 
one  twenty-fifth  of  an  inch. 

Such  a  combination  of  levers  is  called  a  compound  lever. 

QUESTIONS  ON  THE  LEVER. 

80.  In  a  lever,  the  power  arm  is  18  inches  and  the  weight  arm 
is  42  inches.     What  weight  would  be  balanced  by  60  pounds  of 
power? 

Denote  the  power  arm  by  PA,  and  the  weight  arm  by  W  A. 

PA=%  WA 
...  VP  =  $  VW 
.:  P  =  \  W 
60  =  |  W 
60-^  =  25* 

W —  254  pounds. 

8 1.  In  a  lever,  the  power  arm  is  36  inches,  and  the  weight  arm 
27  inches.     What  power  will  balance  a  weight  of  75  pounds  ? 

82.  In  a  lever,  the  power  arm  is  14  decimetres  long,  and  the 
weight  arm  21   decimetres.     What  weight  would  be  balanced 
by  70  grammes  of  power? 

83.  In  a  lever,  the  power  arm  is  49  decimetres  long,  and  the 
weight  arm  28  decimetres.     What  power  would  balance  a  weight 
of  17  kilogrammes  ? 

84.  In  a  lever,  a  power  of  30  pounds  balances  a  weight  of 
50  pounds,  and  the  power  arm  is  80  inches  long.     What  is  the 
length  of  the  weight  arm  ? 

85.  In  a  lever,  a  power  of  70  pounds  balances  a  weight  of 
20  pounds,  and  the  weight  arm  is  30  inches  long.     What  is  the 
length  of  the  power  arm  ? 

86.  In  a  lever,  a  power  of  150  grammes  balances  a  weight  of 
250  grammes,  and  the  power  arm  is  18  decimetres  in  length. 
What  is  the  length  of  the  weight  arm  ? 

87.  In  a  lever,  a  power  of  270  grammes  balances  a  weight  of 
1 20  grammes,  and  the  weight  arm  is  48  decimetres  in  length. 
What  is  the  length  of  the  power  arm  ? 


60  NATURAL    PHILOSOPHY. 

88.  In  a  lever  of  the  first  order,  a  power  of  30  pounds  bal- 
ances a  weight  of  40  pounds,  and  the  power  arm  is  27  inches 
long.     What  is  the  length  of  the  lever  ? 

89.  In  a  lever  of  the  first  order,  a  power  of  55  grammes  bal- 
ances a  weight  of  35  grammes,  and  the  weight  arm  is   13  deci- 
metres long.     What  is  the  length  of  the  lever  ? 

90.  In  a  lever  of  the  second  order,  a  power  of  16  pounds 
balances  a  weight  of  56  pounds,  and  the  length  of  the  weight 
arm  is  34  inches.     What  is  the  length  of  the  lever  ? 

91.  In  a  lever  of  the  second  order,  the  length  of  the  lever  is 
65  decimetres,  and  a  power  of  24  grammes  will  balance  a  weight 
of  64  grammes.     What  is  the  length  of  the  weight  arm  ? 

92.  In  a  lever  of  the  third  order,  the  length  of  the  lever  is 
80  inches,  and  the  length  of  the  power  arm  30  inches.     What 
weight  would  be  balanced  by  47  pounds  of  power  ? 

93.  In  a  lever  of  the  third  order,  the  length  of  the  lever  is 
28  decimetres,  and  the  length  of  the  power  arm  is  12  decimetres. 
What  power  will  balance  18  grammes  of  weight  ? 

86.  The  Pulley.  —  The  pulley  is  a  small  grooved  wheel 
arranged  so  as  to  turn  freely  in  a  frame  called  the  block. 
The  pulley  is  an  instrument  in  which  power  is  applied  to 
do  work  by  means  of  a  cord  instead  of  a  bar,  as  in  the 
case  of  the  lever.     The  wheel  of  the  pulley  serves  simply 
to  diminish  friction  at  the  points  over  which  the  cord  is 
drawn. 

Fig.  4i.  In  Figure  41,  the  block  of  the  pulley  D  C 

is  fastened  to  the  beam  above,  so  as  to  be 
stationary,  while  the  block  of  the  pulley 
A  B  is  free  to  move  up  and  down.  The 
former  is  called  -A.  fixed  pulley  ;  and  the  latter, 
a  movable  pulley.  A  fixed  pulley  serves 
P  simply  to  change  the  direction  in  which  the 
power  acts. 

87.  Systems  of  Pulleys  with  one  Cord.  —  In  Figures  42, 
43,  and   44,   are  shown  systems  of  pulleys  with  a  single 
cord,    that   is,    in   which   one    cord    passes   over   all  the 


NATURAL    PHILOSOPHY. 


6  I 


pulleys.     The   power  is  applied  to  the  end  of  the  rope, 
and  the  weight  is  attached   to  the  movable  block.      In 


the  first  case,  on   raising  the   movable 

block  one  inch,  three   inches   of    rope 

will  be  released,  since  the  rope  comes 

three  times  to  that  block.     In  this  case 

the  power  will  move  three  times  as  fast 

as  the  weight.     In  the  second  case,  on 

raising  the  movable  block  one  inch,  four  inches  of  rope 

will  be  released,  since  the  rope  comes  four  times  to  this 

block.     In  this  case  the  power  will  move  four   times   as 

fast   as   the    weight.      In  the    third  case    the   power  will 

move  six  times  as  fast  as  the  weight. 

The  special  law  of  a  system  of  pulleys  with  a  single 
rope  is  that  the  velocities  of  the  po^ver  and  weight  are  in  the 
inverse  ratio  of  the  number  of  times  the  rope  comes  to  each. 
As  the  cord  always  comes  once  to  the  power,  the  power 
will  balance  a  weight  as  many  times  itself  as  the  rope 
comes  times  to  the  block  bearing  the  weight. 


NATURAL    PHILOSOPHY. 


QUESTIONS  ON  PULLEYS    WITH  SINGLE  ROPE. 

94.  In  a  system  of  pulleys  with  a  single  rope,  the  rope  conies 
13  times  to  the  block  bearing  the  weight.     What  weight  would 
be  balanced  by  75  pounds  of  power  ? 

95.  In  a  system  of  pulleys  with  a  single  cord,  the  cord  comes 
9  times  to  the  block  bearing  the  weight.     What  power  would 
balance  19  grammes  of  weight  ? 

96.  In  a  system  of  pulleys  with  a  single  rope,  a, power  of  13 
pounds  balances  a  weight  of  91  pounds.     How  many  times  does 
the  rope  come  to  the  block  bearing  the  weight? 

97.  In  a  system  of  pulleys  with  a  single  rope,  a  power  of  72 
grammes  balances  a  weight  of  792  grammes.     How  many  times 
does  the  rope  come  to  the  block  bearing  the  weight? 

88.  Systems  of  Pulleys  -with  more  than  one  Rope.  —  The  law 
of  the  pulley  is  sometimes  stated  as  follows  :  A  stretched  rope 
must  have  the  same  tension  throughout  its  whole  length. 

Figure  45  represents  a  system  of  pulleys  in  which  two  ropes 
are  used.  Here  a  weight  of  four  pounds  is  balanced  by  a  power 


Fig.  45.  of  one  pound.  The  parts  of  the  rope 
A  D  and  A  B  must  each  have  a  ten- 
sion equal  to  the  power.  The  rope 
A  C B  balances  the  two  tensions,  B  P 
and  B  A,  and  must  therefore  have  a 
tension  of  twice  the  power.  The  three 
tensions  supporting  the  pulley  A 
amount  therefore  to  four  times  the 
power. 

In  the  system  shown  in  Figure  46 
four  ropes  are  used.  The  tensions  of 
the  several  ropes  will  be  readily  un- 
derstood from  the  numbers.  It  will 
be  seen  that  in  this  case  the  power  is 
doubled  by  each  movable  pulley  which  is  added  : 


F.g.  46. 


but,  as  in  a 


the  systems  we  have  examined,  what  is  gained  in  power  is  lost 
in  speed. 

89.  Wheel  and  Axle. — The  wheel  and  axle  consists  of 
a  wheel,  or  drum,  A  (Figure  47),  mounted  on  an  axle  J3, 
The  power  and  weight  are  applied  to  ropes  which  pass, 


NATURAL   PHILOSOPHY.  63 

one  over  the  wheel  and  the  other  over  the  axk,  in  opposite 
directions,  so  that  one  unwinds  as  the  other  winds  up. 
Fig.  47.  The  power  and  weight  are  really  ap- 

plied to  the  wheel  and  axle  at  the 
point  where  the  rope  touches  each, 
that  is,  at  the  end  of  the  radius  of 
each.  The  one  applied  to  the  wheel 
r  I  moves  the  faster,  and  just  as  many 

y  times  faster  as  the  circumference  or 

/  the  radius  of  the  wheel  is  times  the  cir- 

cumference or  the  radius  of  the  axle. 

The  special  law  of  the  wheel  and  axle  is  that  the  veloci- 
ties of  the  power  and  weight  are  in  the.  direct  ratio  of  the 
radii  to  which  they  are  applied.  When  the  power  is  applied 
to  the  wheel,  there  is  a  gain  of  power;  and  when  it  is 
applied  to  the  axle,  there  is  a  loss  of  power. 

The  chief  use  of  the  wheel  and  axle  in  machinery  is  in 
transmitting  motion  of  rotation  from  one  piece  to  another, 
with  or  without  a  change  of  velocity.  For  an  increase  of 
velocity,  a  large  wheel  must  act  upon  a  small  one  \  and  for  a 
diminution  of  velocity,  a  small  wheel  must  act  upon  a  large 
one.  When  there  is  to  be  no  change  of  velocity,  the  wheels 
must  both  be  of  the  same  size.  Fig  ^ 

90.  Cog-  Wheels.  —  There 
are  various  ways  in  which  the 
axle  of  one  wheel  is  made 
to  act  on  the  circumference 
of  another.  Sometimes  the 
one  turns  the  other  by  rub- 
bing against  it,  or  by  friction. 
The  most  common  way, 
however,  is  by  means  of 
teeth  or  cogs  raised  on  the 
surfaces  of  the  wheels  and 
axles.  The  cogs  on  the 


64 


NATURAL    PHILOSOPHY. 


wheel  are  usually  called  teeth,  while  those  on  the  axle  are 
called  leaves,  and  the  part  of  the  axle  from  which  they  pro- 
ject is  called  thermion. 

91.  The  Gain  of  Power  by  Wheel-  Work.  —  In  the  train  of 
wheels  in  Figure  48,  if  the  circumference  of  the  wheel  a 
is  36  inches,  and  that  of  the  pinion  b  is  9  inches,  or  one 
fourth  as  great,  a  power  of  one  pound  at  P  will  exert  a 
force  of  four  pounds  on  b.  If  the  circumference  of  the 
wheel  e  is  30  inches,  and  that  of  the  pinion  C  10  inches, 
the  four  pounds  acting  on  the  former  will  exert  a  force  of 
twelve  pounds  on  the  latter.  If  the  circumference  of  the 
wheel  /  is  40  inches,  and  that  of  the  axle  d  8  inches,  the 
twelve  pounds  acting  on  /  will  exert  a  force  of  sixty 
pounds  on  d.  One  pound  at  P  will  then  balance  sixty 
pounds  at  W. 

But  in  this  case,  as  in  all  others,  what  is  gained  in  power 
is  lost  in  speed;  since  the  one  pound  at  /'must  move 
through  sixty  inches  in  order  to  raise  the  sixty  pounds  at 
W  one  inch. 

Cog-wheels  which  have  their  teeth  arranged  as  in  Figure 
48  are  called  spur-wheels.  If  the  teeth  project  from  the 

Fig.  49-  Fig.  50. 


side  of  the  wheel,  as 

in    Figure    49,    it    is 

called  a  crown-wheel. 

If    their    edges    are 

sloped,  as  in  Figure  50,  the  wheel  is  called  a  bevel-wheel. 

Bevel-wheels  may  be  inclined  to  each  other  at  any  angle. 


NATURAL   PHILOSOPHY.  65 

In  all  cases  the  lines  which  mark  the  slope  of  the  teeth  of  the 
two  wheels  will  meet  at  the  same  point,  as  in  ^Figure  50. 

92.  Belted  Wheels.  —  Another  way  in  which  wheels  and 
axles  may  be  made  to  act  upon  one  another  is  by  means 
of  a  belt,  or  band,  passing  over  them  both.  They  may 
thus  be  at  any  distance  apart,  and  may  turn  either  the 
same  way  or  contrary  ways,  according  as  the  belt  does  or 

Fig.  51.  Fig.  52. 


Fig-  S3. 


does  not  cross  between  them  (Figures  51  and  52).  A  cog- 
wheel and  its  pinion  must,  of  course,  always  turn  in  con- 
trary directions. 

93.  The  Windlass  and  Capstan.  —  The  windlass  is  a 
horizontal  barrel  turned  by  means 
of  a  crank  or  spokes  (Figure 
53).  It  may  be  regarded  as  a 
modification  of  the  wheel  and 
axle,  the  crank  taking  the  place 
of  the  wheel.  The  capstan  is  an 

upright  drum  turned  by  means  of          ' ' 

levers,  which  may  be  removed  at  pleasure. 

QUESTIONS  ON   THE    WHEEL  AND  AXLE. 

98.  The  radius  of  a  wheel  is  40  inches,  and  that  of  its  axle 
15  inches.  What  weight  on  the  axle  would  be  balanced  by  50 
pounds  of  power  on  the  wheel  ? 

Denote  the  radius  of  the  wheel  by  R  W,  and  that  of  the 
axle  by  R  A. 


=      VW 


5°  -T-  I  =  I33i 

W  '=  133$  pounds. 


66 


NATURAL    PHILOSOPHY. 


99.  The  radius  of  a  wheel  is  18  decimetres,  and  that  of  its 
axle  12  decimetres.     What,  weight  on  the  wheel  would  be  bal- 
anced by  32  grammes  of  power  on  the  axle  ? 

100.  In  a  wheel  and  axle,  a  power  of  63  pounds  on  the  axle 
balances  a  weight  of  35  pounds  on  the  wheel.     The  radius  of 
the  wheel  is  16  decimetres.     What  is  the  radius  of  the  axle  ? 

101.  A  power  of  21  pounds  on  the  wheel  balances  a  weight 
of  77  pounds  on  the  axle.     The  radius  of  the  axle  is  5  inches. 
What  is  the  radius  of  the  wheel  ? 


94.  The  Inclined  Plane.  —  An  inclined  plane  is  simply  an 
inclined  surface.  It  is  easier  to  roll  a  body  up  an  inclined 
surface  than  to  raise  the  body  vertically  to  the  same 
height.  The  longer  the  plane,  the  easier  it  is  to  roll  the 
body  up  it.  The  reason  is  obvious.  The  body  must  be 
raised  against  the  action  of  gravity ;  and  by  rolling  the 
body  up  the  inclined  surface,  the  power  is  compelled  to 
act  the  length  of  the  surface  to  raise  the  weight  the  height 
of  it. 

The  special  law  of  the  inclined  plane  is  that  the  velocities 
of  the  power  and  weight  are  in  the  ratio  of  the  length  of  the 
plane  to  its  height.  Since  the  power,  and  weight  are  in  the 
inverse  ratio  of  their  velocities,  it  follows  that  the  power 
will  be  to  the  weight  as  the  height  of  the  plane  is  to  its  length. 

The  law  of  the  inclined  plane  may  be  demonstrated  by 
means  of  the  apparatus  represented  in  Figure  54.  R  S  rep- 
resents the  section  of  a 


Fig.  54- 


smooth  piece  of  hard  wood 
hinged  it  R ;  by  means  of 
a  screw  it  can  be  clamped 
at  any  angle  x  against  the 
arc-shaped  support ;  a  is  a 
metal  cylinder,  to  the  axis 
of  which  is  attached  a  string 
passing  over  a  pulley  to  a 
scale-pan  P. 


NATURAL    PHILOSOPHY.  67 

It  is  thus  easy  to  ascertain  by  direct  experiments  what 
weight  must  be  placed  in  the  pan  P  in  order  to  balance 
a  roller  of  any  given  weight. 

The  line  R  S  represents  the  length,  S  T  the  height,  and 
R  Tihe  base  of  the  inclined  plane. 

In  ascertaining  the  conditions  of  equilibrium  we  have  a  use- 
ful application  of  the  parallelogram  of  forces.  Let  the  line  a  b 
(Figure  54)  represent  the  force  which  the  weight  W  of  the  cylin- 
der exerts  acting  vertically  downward;  this  may  be  decomposed 
into  two  others,  —  one,  ad,  acting  at  right  angles  against  the 
plane,  and  representing  the  pressure  which  the  weight  exerts 
against  the  plane,  and  which  is  counterbalanced  by  the  reaction 
of  the  plane  ;  the  other,  ac,  representing  the  component  which 
tends  to  move  the  weight  down  the  plane,  and  which  has  to  be 
held  in  equilibrium  by  the  weight,  P,  equal  to  it  and  acting  in 
the  opposite  direction. 

It  can  be  readily  shown  that  the  triangle  abc\s  similar  to 
the  triangle  S  R  7",  and  that  the  sides  a  c  and  a  b  are  in  the  same 
proportion  as  the  sides  S  T  and  S  R.     But  the  line  ac  repre- 
sents the  power,  and  the  line  a  b  the  weight ;  hence 
ST:  SR  =  P  :  W. 

95.  The  Wedge.  —  Instead  of  lifting  a  weight  by  moving 
it  along  an  inclined  plane,  we  may  do  the  same  thing  by 
pushing  the  inclined  plane  under  the  weight.     When  used 
in  this  way  the   inclined   plane  is  called   the  wedge.     A 
wedge  which  is  used  for  splitting  wood  has       Fig.  55. 
usually  the  form  of  a  double  inclined  plane, 

as  in  Figure  55.  The  law  of  the  wedge  is  the 
same  as  that  of  the'inclined  plane,  but  since 
a  wedge  is  usually  driven  by  a  blow  instead 
of  a  force  acting  continuously,  it  is  difficult  to 
illustrate  this  law  by  experiments. 

96.  Uses  of  the  Wedge. — The  wedge  is  es- 
pecially useful  when  a  large  weight  is  to  be 

raised  through  a  very  short  distance.    Thus,  a  tall  chimney, 
the  foundation  of  which  has  settled  on  one  side,  has  been 


68  NATURAL    PHILOSOPHY. 

made  upright  again  by  driving  wedges  under  that  side. 
So,  too,  ships  are  often  raised  in  docks  by  driving  wedges 
under  their  keels.  -Cutting  and  piercing  instruments,  such 
as  razors,  knives,  chisels,  awls,  pins,  needles,  and  the  like, 
are  different  forms  of  wedges. 

97.  The  Screw.  —  In    Figure  56,  we  have   a  machine 
called  the  screw.     It  is  a  movable  inclined  plane,  in  which 

Fig.  56.  the  inclined  surface  winds  round  a 

cylinder.  The  cylinder  is  the  body 
of  the  screw,  and  the  inclined  sur- 
face is  its  thread. 

The  screw  usually  turns  in  a 
block  N,  called  the  nut.  Within 
the  nut  there  are  threads  exactly 
corresponding  to  those  on  the 
screw.  The  threads  of  the  screw 
move  in  the  spaces  between  those 
of  the  nut. 

The  power  is  usually  applied  to 
the  screw  by  means  of  a  lever  P.  Sometimes  the  screw  is 
fixed  and  the  nut  is  movable,  and  sometimes  the  nut  is 
fixed  and  the  screw  movable. 

98.  Hunter's  Screw.  —  In  Figure  56,  if  we  turn  the  lever  P 
round  once,  the  weight  W  will  be  raised  a  distance  equal  to  the 
space  between  two  threads  of  the  screw.     Were  the  lever  of 
such  a  length  that  its  end  would  describe  a  path   10  feet  long, 
and  were  the  distance  between  two  threads  of  the  screw  %  of  an 
inch,  and  were  there  no  friction  in  the  nut,  a  power  of  one  pound 
applied  to  the  end  of  the  lever  would  exert  a  force  of  480  pounds 
upon  the  weight.     It  will  be  seen  from  this  that  the  mechanical 
advantage  of  the  screw  may  be  increased   by  increasing   the 
length  of  the  lever  by  which  it  is  turned,  or  by  bringing  the 
threads  closer  together.      But  if  the  threads  are  brought  too 
near  together,  they  become  too  weak  ;  while,  on  the  other  hand, 
the  machine  becomes  unwieldy  if  the  lever  is  made  too  long. 
These  objections  have  been  obviated  in  the  differential  screw, 


NATURAL    PHILOSOPHY. 


69 


Fig.  57. 


contrived  by  Hunter,  and  shown  in  Figure  57.  W  is  the  nut  in 
which  the  screw  A  plays.  We  will  suppose  that  the  threads 
of  this  screw  are  ^  of  an  inch  apart. 
This  screw  A  is  a  hollow  nut,  which  re- 
ceives the  smaller  screw  ff,  the  threads  of 
which  we  will  suppose  to  be  ^r  of  an  inch 
apart.  This  small  screw  is  free  to  move 
upward  and  downward,  but  is  kept  from 
turning  round  by  means  of  the  framework. 
If  by  means  of  the  handle  the  larger  screw 
is  turned  round  ten  times,  and  the  smaller 
screw  is  allowed  to  turn  round  with  it,  the 
point  W  will  rise  an  inch.  If  we  then 
turn  the  smaller  screw  ten  times  backward, 
the  point  IV  will  move  down  \\  of  an  inch. 
The  effect  of  both  these  motions  will  be  to  raise  the  point  W 
-jJy  of  an  inch.  But  if  the  smaller  screw  has  been  turned 
upward  ten  times  and  then  downward  ten  times,  the  effect  is  the 
same  as  if  it  had  been  kept  from  turning.  Hence,  by  turning 
the  lever  round  ten  times,  the  point  W  will  be  raised  ^  of  an 
inch,  or  the  difference  of  the  distances  between  the  threads  in 
the  two  screws,  while  the  point  E  has  been  raised  an  inch. 
According  to  the  law  of  machines,  then,  the  pressure  at  W  is 
eleven  times  as  great  as  at  E. 

99.    The  Endless  Screw.  —  In  Figure  58,  the  thread  of 


the  screw  works  between  the  teeth  of  the 
wheel.  Hence,  if  the  screw  is  turned, 
the  wheel  must  turn.  Since  as  fast  as 
the  teeth  at  the  left  escape  from  the 
screw  those  on  the  right  come  up  to  it, 
the  screw  is  acting  upon  the  wheel  con- 
tinually: Hence  this  machine  is  called 
the  endless  screw. 


Fig.  58. 


III. 

PHYSICS. 

I. 

STATES   OF   MATTER. 

A.   THREE  STATES  OF  MATTER. 

100.  The  Three  States.  —  Matter  exists  in  three  different 
states,  known  as  the  solid,  the  liquid,  and  the  gaseous.     Ice 
is  a  solid,  water  is  a  liquid,  and  steam  and  air  are  gases. 
While  the  substance  of  a  body  depends  upon  its  atomic 
structure,  the  state  of  a  body  depends  upon  its  molecular 
structure.     Hence  the  state  of  matter  is  a  physical  condi- 
tion, and  changes  of  state  are  physical  changes. 

1 01.  Cohesion  in  the  Different  States  of  Matter.  —  The 
different  states  of  matter  depend  upon  the  strength  of  the 
attraction  of  cohesion  among  the  molecules.     This  is  com- 
paratively strong  in  solids,  very  weak  in  liquids,  and  en- 
tirely wanting  in  gases.     The  molecules  of  some  solids  are 
bound  together  much  more  firmly  than  those  of  others  by 
cohesion  ;  but  even  when  this  bond  is  weakest,  the  mole- 
cules manifest  a  disposition  to  maintain  their  relative  posi- 
tions in  the  body,  and  the  body  to  preserve  its  form.     In 
liquids,  the  bond  of  cohesion  is  so  slight  that  the  mole- 
cules manifest  no  disposition    to   maintain    their  relative 
positions  in  the  body,  nor  does  the  body  tend  to  preserve 
its  form".     Gases  are  not  held  together  at  all  by  cohesion, 
but  only  by  gravity. 


NATURAL    PHILOSOPHY.  71 

102.  Molecular  Motion  in  the  Different  States  of  Mat- 
ter.—  The  molecules  are,  undoubtedly,  in  incessant  motion 
in  every  state  of  matter,  but  their  freedom  of  motion  is 
very  different  in  the  different  states.  In  solids,  the  mole- 
cules, when  left  to  themselves,  have  fixed  positions,  within 
which  they  can  move  to  a  limited  extent,  but  from  which 
they  can  never  escape.  When  left  to  themselves,  the  mole- 
cules of  a  solid  never  move  around  among  themselves  so 
as  to  change  their  relative  positions.  A  molecule  in  the 
interior  of  a  mass  can  never  work  its  way  to  the  surface, 
nor  can  one  at  the  surface  work  its  way  into  the  interior. 

In  liquids,  the  molecules  are  all  the  time  moving  about 
among  themselves  in  the  interior  of  the  mass  with  the 
utmost  freedom.  No  molecule  is  confined  within  particu- 
lar limits  within  the  mass,  but  every  molecule  is  continu- 
ally moving  to  and  fro  in  every  direction  throughout  the 
entire  mass.  They,  however,  never  escape  from  the  influ- 
ence of  cohesion.  So  long  as  they  are  in  the  interior  of 
the  mass,  the  cohesion  of  the  molecules  on  one  side  of  them 
is  exactly  balanced  by  that  of  the  molecules  on  the  other 
side ;  hence  it  does  not  interfere  with  the  freedom  of  their 
motion.  But  as  the  molecules  come  to  the  surface,  they 
experience  only  the  pull  of  the  molecules  behind  them,  and 
this  is  usually  sufficient  to  stop  their  outward  motion  and 
to  cause  them  to  return  into  the  interior  of  the  mass.  In 
gases,  the  molecules  are  moving  without  the  slightest  re- 
straint from  cohesion  ;  hence  they  move  in  straight  lines. 
They  are  continually  striking  together  and  rebounding 
again,  but  after  each  rebound  they  move  in  straight  lines 
till  they  encounter  other  molecules.  There  is  no  force  act- 
ing within  the  mass  of  a  gas  which  tends  to  check  the  motion 
of  the  molecules  at  any  point ;  hence  gases  do  not,  like 
liquids,  tend  to  assume  a  definite  surface. 

103.  The  Distances  between  the  Molecules  in  the  Different 
States  of  Matter.  —  As  a  rule,  the  molecules  are  nearer  to- 


72  NATURAL    PHILOSOPHY. 

gather  in  solids  than  in  liquids,  and  in  liquids  than  in 
gases.  The  molecules  of  steam  are  about  seventeen  hun- 
dred times  as  far  apart  as  those  of  water. 

104.  Behavior  of  the  Different  States   of  Matter  when 
Small  Portions  of  each  are  placed  in  Empty  Vessels.  —  If   a 
small  portion  of  a  solid  is  placed  in  an  empty  vessel,  it  will 
either  not  conform  to  the  shape  of  the  vessel  at  all,  or,  in 
the  case  of  a  soft  solid,  only  slowly  and  imperfectly.     This 
is  owing  to  the  tendency  of  a  solid  to  maintain  its  shape. 
If  a  small  amount  of  a  liquid  is  put  into  an  empty  vessel, 
it  will  conform  at  once  and  perfectly  to  the  shape  of  the 
vessel,  but  it  will  not  completely  fill  it.     The  liquid  will 
sink  to  the  lowest  part  of  the  vessel,  and  will  be  separated 
by  a  definite  surface  from  the  space  in  the  upper  part  of  the 
vessel.     This  is  because  the  cohesion  of  the  liquid  checks 
the  outward  motion  of  the  molecules,  and  so  keeps  them 
from  moving  away  from  the  mass.     If  any  portion  of  a  gas, 
however  small,  is  placed  in  an  empty  vessel,  however  large, 
the  gas  will  completely  fill  the  vessel.      This  is  because 
there  is  nothing  to  check  the  outward  motion  of  the  mole- 
cules of  the  gas,  save  the  walls  of  the  vessel  in  which  it  is 
inclosed. 

B.    FLUIDS. 

105.  Fluids.  —  Owing  to  their  freedom  of  molecular  mo- 
tion, liquids  and  gases  have  several  characteristics  in  com- 
mon.     They  are,  accordingly,  often  classed    together   as 
fluids.     This  appellation  is  derived  from  the  readiness  with 
which  portions  of  each  of  these  states  of  matteryfoo/  over 
or  among  each  other. 

1 06.  Pascal's  Law.  —  One  of  the  most  remarkable  char- 
acteristics of  a  fluid  is  the  way  in  which  it  transmits   any 
pressure  that  is  brought  to  bear  on  it.     If  any  pressure  is 
brought  to  bear  on  any  portion  of  the  surface  of  a  fluid  which 
fills  a  closed  vessel,  a  pressure  just  equal  to  it  will  be  transmit- 
ted through  the  fluid  to  every  equal  portion  of  surface.     This 


NATURAL    PHILOSOPHY. 


73 


law  was  enunciated  by  Pascal,  and  is  known  as  Pascal's 
law. 

The  following  experiment  shows  that  pressure  is  trans- 
mitted in  all  directions  by  a  fluid.  A  tube  (Figure  59)  is 
provided  with  a  piston  and  Fig.  59. 

fitted  with  a  hollow  globe, 
which  is  pierced  with  a  num- 
ber of  orifices,  arranged  in  a 
circle  around  it.  Fill  the 
globe  and  tube  with  water. 
If  the  piston  is  forced  in,  the 
water  spouts  out  of  all  the  orifices,  and  not  merely  those 
opposite  the  piston. 

Conceive  a  vessel  of  any  form,  in  the  sides  of  which  are 
a  number  of  cylindrical  apertures,  all  of  the  same  size,  and 
closed  with  movable  pistons,  as  shown  at 
A,  B,  C,  D,  and  E  (Figure  60).  Suppose  a 
pound  of  pressure  brought  to  bear  upon 
A.  A  pound  of  pressure  will  be  trans- 
mitted to  each  of  the  other  pistons  in  the 
direction  of  the  arrows.  If  the  piston  B 
had  only  half  the  surface  of  A,  it  would 
receive  only  ^  a  pound  of  pressure  ;  if  it 
had  twice  the  surface  of  A,  it  would  receive  2  pounds  of 
pressure  ;  if  it  had  three  times  the  surface  of  A,  it  would 
receive  3  pounds  of  pressure  ;  and  so  on. 

1 07.  The  Hydraulic  Press.  — It  follows,  from  what  has  just 
been  shown,  that  by  means 
of  a  liquid  a  small  pressure 
upon  a  small  surface  may 
be  made  to  exert  a  great 
pressure  upon  a  large  sur- 
face. In  Figure  61  we 
have  two  cylinders,  with  a 
piston  in  each.  Suppose 


Fig.  6, 


74 


NATURAL   PHILOSOPHY. 


that  the  surface  of  the  larger  piston  is  fifty  times  that  of  the 
smaller;  if  the  latter  is  pressed  downward  by  a  weight  of  one 
pound,  an  upward  pressure  of  one  pound  will  be  brought 
to  bear  upon  each  portion  of  the  surface  of  the  large  piston 
equal  to  that  of  the  small  piston.  The  whole  upward  pres- 
sure on  the  large  piston  will  then  be  fifty  times  the  down- 
Fig.  62. 


ward  pressure  on  the  small  one.  If  the  surface  of  the 
larger  piston  had  been  one  hundred  times  that  of  the 
smaller,  one  pound  on  the  latter  would  have  balanced  one 
hundred  on  the  former;  and  so  on. 

The  hydraulic  press  is  constructed  on  the  principle  illus- 
trated above.      One  form  of  this  press  is  shown  in  Fig- 


NATURAL    PHILOSOPHY. 


75 


ures  62  and  63.  The  two  cylinders  A  and  B  are  connected 
by  the  pipe  d.  The  piston  a,  in  the  cylinder  A,  is  worked 
by  the  handle  O,  and  forces  water  into  the  large  cylinder  J3, 
where  it  presses  up  the  piston  C.  If  the  end  of  the  piston  C 
is  1000  times  as  large  as  that  of  the  piston  a,  a  pressure  of 
2  pounds  on  a  would  exert  a  pressure  of  2000  pounds,  or 
one  ton,  upon  C.  If  a  man,  in  working  the  handle  O,  forces 
clown  the  piston  a  with  a  pressure  of  50  pounds,  he  would 
bring  to  bear  upon  C  a  pressure  of  25  tons. 

This  press  is  used  for  pressing  cotton,  hay,  cloth,  etc., 
into  bales ;  for  extracting  oil  from  seeds  ;  for  testing  can- 
non, boilers,  etc. ;  and  for  raising  ships  out  of  the  water. 

The  hydraulic  jack  is  a  form  of  the  hydraulic  press, 
adapted  to  raising  heavy  weights. 

Fig.  63. 


1 08.  Archimedes 's  Principle.  —  A  body  in  a  fluid  is  buoyed 
up  by  a  force  equal  to  the  weight  of  the  fluid  it  displaces. 
This  fact  was  discovered  by  Archimedes,  and  is  therefore 
designated  by  his  name. 

Archimedes's  principle  may  be  verified  by  the  following 
experiment.  A  brass  cylinder  is  constructed  so  as  just  to 
fill  a  cup.  The  cup  and  cylinder  are  hung  from  one  pan 


;6  NATURAL   PHILOSOPHY. 

of  a  balance  (Figure  64)  and  counterpoised  in  the  air  by 
weights  in  the  other  pan.  The  cylinder  is  then  allowed  to 
hang  in  a  vessel  of  water.  The  weights  overbalance  the 
cup  and  cylinder,  showing  that  the  water  lifts  the  cylinder 
up.  Equilibrium  is  restored  by  filling  the  cup  with  water. 
When  the  cup  is  full,  the  beam  of  the  balance  will  be  hor- 
izontal, and  the  cylinder  will  be  completely  in  the  water, 
showing  that  the  cylinder  is  buoyed  up  by  the  water  with  a 
force  equal  to  the  weight  of  the  cup  full  of  water,  or  to 
the  weight  of  the  water  displaced  by  the  cylinder. 

Fig.  64. 


109.  Forces  acting  upon  a  Body  immersed  in  a  Fluid.  — 
Every  body  immersed  in  a  fluid  is  subjected  to  two  forces  : 
one  equal  to  its  own  weight,  which  tends  to  make  the  body 
sink  ;  the  other  equal  to  the  weight  of  the  liquid  displaced, 
which  tends  to  make  the  body  rise. 

When  a  body  displaces  more  than  its  own  weight  of  a 
fluid,  it  will  rise  in  that  fluid  ;  when  it  displaces  less  than  its 
own  weight,  it  will  sink  ;  and  when  it  displaces  just  its  own 
weight,  it  will  remain  suspended  wherever  it  happens  to  be. 


NATURAL    PHILOSOPHY. 


77 


These  three  cases  may  be  illustrated  by  putting  an  egg 
into  salt  and  fresh  water  (Figure  65).     When  the  egg  is 

Fig.  65. 


Fig.  66. 


placed  in  salt  water,  it  rises  to  the  surface  because  it  dis- 
places more  than  its  own  weight  of  the  brine.  When  it  is 
put  into  the  fresh  water,  it  sinks  to  the  bottom  because  it 
displaces  less  than  its  own  weight  of  the  water.  When 
it  is  put  into  a  proper  mixture  of  fresh  water  and  brine,  it 
will  remain  suspended  in  the 
fluid,  because  it  displaces  just 
its  own  weight  of  the  mixture. 
1 10.  Floating  Bodies.  —  Ev- 
ery body  floating  in  a  fluid 
displaces  just  its  own  weight 
of  the  fluid.  This  is  equally 
true  of  a  ship  floating  in  water, 
or  a  balloon  floating  in  the  air 
(Figure  66).  The  more  heavily 
the  ship  is  loaded,  the  deeper 
she  sinks  into  the  water.  By 
throwing  out  the  sand  which  is 
used  as  ballast,  the  balloon 
is  made  lighter,  so  as  to  dis- 
place more  than  its  own  weight 
of  air.  It  then  rises  till  it 
comes  into  more  highly  rarefied 


NATURAL    PHILOSOPHY. 


Fig.  67. 


air,  where  it  displaces  just  its  own  weight,  when  it  again 
floats  along  at  the  same  level.  By  opening  the  valve,  so 
as  to  allow  some  of  the  gas  to  escape,  the  balloon  becomes 
less  in  bulk,  and  so  displaces  less  than  its  own  weight  of 
air.  It  then  sinks  until  it  again  displaces  its  own  weight. 

The  appendage  at  the  side  of  the  balloon  (Figure  66)  is 
called  a  parachute.  The  object  of  the  parachute  is  to  allow 
the  aeronaut  to  leave  the  balloon,  by  giving  him  the  means 
of  lessening  the  rapidity  of  his  de- 
scent. It  consists  of  a  large  circu- 
lar piece  of  cloth  (Figure  6?)  about 
1 6  feet  in  diameter,  which,  by  the 
resistance  of  the  air,  spreads  out 
like  a  gigantic  umbrella.  In  the 
centre  there  is  an  aperture,  through 
which  the  air,  compressed  by  the 
rapidity  of  the  descent,  makes  its 
escape ;  for  otherwise  oscillations 
might  be  produced,  which,  when 
communicated  to  the  boat,  would 
be  dangerous. 

In  Figure  66,  the  parachute  is  attached  to  the  network 
of  the  balloon  by  means  of  a  cord,  which  passes  round  a 
pulley,  and  is  fixed  at  the  other  end  to  the  boat.  When 
the  cord  is  cut  the  parachute  sinks,  at  first  very  rapidly, 
but  more  slowly  as  it  becomes  distended,  as  represented  in 
the  figure. 

in.  Equilibrium  of  Floating  Bodies.  —  The  point  of  appli- 
cation of  the  resultant  of  the  upward  pressure  of  a  fluid  upon 
the  various  parts  of  a  floating  body  is  called  the  centre  of  buoy- 
ancy. In  Figures  68  and  69,  the  centre  of  gravity  of  the  float- 
ing body  is  marked'  G,  and  the  centre  of  buoyancy  O ;  and  the 
direction  in  which  the  resultants  of  gravity  and  buoyancy  act 
upon  these  points  is  indicated  by  the  arrows. 

In  order  that  a  floating  body  be  in  equilibrium,  it  is  necessary 
that  it  should  displace  its  own  weight  of  the  fluid,  and  that  the 


NATURAL   PHILOSOPHY.  79 

centres  of  gravity  and  buoyancy  should  be  on  the  same  vertical 
line.  Unless  the  latter  condition  is  fulfilled,  the  forces  of  gravity 
and  buoyancy  would  tend  to  turn  the  body  over.  This  is  evi- 
dent from  Figure  68.  When  a  body  is  completely  immersed  in  a 
fluid,  it  can  be  in  stable  equilibrium  only  when  its  centre  of 
gravity  is  below,  the  centre  of  buoyancy,  for  in  this  case  only 
would  the  action  of  the  two  forces  tend  to  right  the  body  when 
tipped.  This  is  also  evident  from  Figure  68. 

When  the  body  is  only  partially  immersed,  it  maybe  in  stable 
equilibrium  when  the  centre  of  buoyancy  is  below  the  centre  of 
gravity ;  for  when  the  body  tips,  the  rigure  of  the  liquid  dis- 
placed changes,  and  the  centre  of  buoyancy  shifts  towards  the 
side  on  which  the  body  is  more  deeply  immersed,  so  that  the 
two  forces  may  still  tend  to  right  the  body,  as  shown  in  Figure 

Fig.  68.  Fig.  69. 


69.  The  two  forces  will  tend  to  right  the  body  as  long  as  the 
vertical  from  the  centre  of  gravity  falls  within  the  centre  of 
buoyancy.  If  the  vertical  falls  beyond  the  centre  of  buoyancy, 
the  two  forces  will  tend  to  overturn  the  body.  The  higher  the 
centre  of  gravity,  the  more  likely  the  vertical  to  fall  beyond 
the  centre  of  buoyancy.  Hence  a  small  boat  is  more  likely  to 
upset  when  the  persons  in  it  stand  than  when  they  sit. 

112.  Method  of  finding  the  Specific  Gravity  of  Solids  and 
Liquids.  —  To  find  the  specific  gravity  of  a  solid  or  liquid, 
it  is  necessary  to  find  the  weight  of  a  volume  of  water 
equal  to  that  of  a  portion  of  the  solid  or  liquid  whose 
specific  gravity  is  to  be  found.  By  means  of  Archimedes's 
principle,  the  weight  of  this  volume  of  water  is  easily 
found. 

Suppose  we  wish  to  find  the  specific  gravity  of  copper. 
Fasten  the  piece  of  copper  to  one  pan  of  the  balance  by  a 
fine  thread  (Figure  70),  and  counterpoise  it  in  the  air  with 


8o 


NATURAL   PHILOSOPHY. 


weights  in  the  other  pan.  Suppose  it  to  weigh  125.35 
grains.  Then  suspend  it  in  a  vessel  of  water  and  restore 
the  equilibrium  by  placing  weights  in  the  pan  supporting 
the  copper.  Suppose  it  to  require  14.24  grains.  This, 
according  to  Archimedes's  principle,  is  the  weight  of  the 
water  displaced  by  the  copper,  or  of  a  volume  of  water 
equal  to  that  of  the  copper.  The  specific  gravity  of  the 
copper  is  *££&  =  8-8- 

Fig.  7.. 


When  the  body  whose  specific  gravity  we  wish  to  find 
is  lighter  than  water,  we  must  fasten  it  to  a  heavy  body  to 
sink  it.  We  then  find,  by  the  above  method,  the  weight  of 
the  water  displaced  by  the  sinker  alone,  and  by  the  sinker 
and  light  body  together.  The  difference  between  the  two 
will  be  the  weight  of  the  water  displaced  by  the  lighter 
body. 

The  specific  gravity  of  a  liquid  may  be  found  by  the 
following  method.  A  glass  ball,  weighted  with  mercury  in- 
side, is  first  accurately  weighed  in  air.  It  is  then  immersed 


NATURAL   PHILOSOPHY. 


Si 


in  a  vessel  of  alcohol  or  other  liquid  under  examination 
(Figure  71),  and  equilibrium  is  restored  by  adding  weights 
to  the  pan  from  which  the  ball  is  suspended.  Suppose 
35.43  grains  are  required.  This  will  be  the  weight  of  the 
ball's  volume  of  alcohol.  Next  immerse  the  ball  in  water, 
and  restore  the  equilibrium  as  before.  Suppose  it  requires 
44.28  grains  this  time.  This  will  be  the  weight  of  the 
ball's  volume  of  water.  The  specific  gravity  of  alcohol 
will  be  f5:||  =  .8. 

113.    Nicholson's  Hydrometer.  —  This  instrument  (Figure  72) 
consists  of  a  hollow  cylinder  of  metal  with  conical  ends,  carry- 
Fig.  72. 


ing  a  basket  at  the  bottom  and  supporting  a  small  dish  on  a 
slender  rod  at  the  top.  The  weight  and  volume  of  this  instru- 
ment are  such  that  it  requires  1000  grains  in  the  dish  at  the  top 
to  sink  it  to  a  mark  on  the  rod.  It  may  be  used  for  finding  the 
weights  and  specific  gravities  of  small  bodies. 

The  weight  of  the  small  body  is  found  by  putting  the  body  in 
the  dish  at  the  top,  and  adding  weights  enough  to  sink  the 
instrument  to  the  mark  on  the  rod.  The  difference  between 
these  weights  and  1000  grains  will  be  the  weight  of  the  body 
in  grains.  To  find  the  weight  of  the  water  displaced  by  the 
body,  transfer  it  to  the  basket  at  the  bottom,  and  add  weights 


82 


NATURAL    PHILOSOPHY. 


enough  to  the  dish  again  to  sink  the  instrument  to  the  mark. 
The  weights  added(will  be  the  weight  of  the  water  displaced  by 
the  body.  The  specific  gravity  of  the  body  will  be  its  weight, 
divided  by  the  weight  of  the  water  it  displaces. 

114.    Ordinary   Hydrometers. — These    instruments    are 
usually  of  the  form  shown  in  Figure  73.    They  are  weighted 
Fig.  73.  at  the  lower  end  with  mercury 

to  keep  them  in  an  upright 
position.  The  bulb  above  the 
mercury  causes  them  to  dis- 
place enough  of  a  liquid  to 
float  in  it.  When  put  in  a 
liquid  they  sink  in  it  till  they 
displace  their  own  weight. 
The  deeper  they  sink  in  a 
liquid,  the  less  its  specific 
gravity.  Their  stems  are 
graduated  in  such  a  way  that 
the  number  on  the  stem  at  the 
surface  of  the  liquid  indicates 
the  specific  gravity  of  the  liquid.  This  is  a  convenient, 
but  not  very  accurate  method  of  ascertaining  the  specific 
gravity  of  a  liquid. 

C.   GASES. 

115.  Expansibility  of  Gases.  —  One  of  the  most  marked 
characteristics  of  a  gas  is  its  capacity  for  indefinite  ex- 
pansion. The  tendency  of  a  gas  to  expand  may  be  illus- 
trated by  the  following  experiment.  An  india-rubber  bag 
partially  filled  with  air  is  closed  air-tight  and  placed  under 
the  receiver  of  an  air-pump.  On  exhausting  the  air  from 
the  receiver,  the  bag  fills  out,  as  shown  in  Figure  74. 

The  tendency  of  a  gas  to  expand  is  due  to  two  facts ; 
namely,  that  the  molecules  of  a  gas  are  not  held  together 
by  cohesion,  and  that  they  are  moving  rapidly  in  straight 


NATURAL    PHILOSOPHY.  83 

lines.  The  condition  of  a  gas  in  a  closed  vessel  has  been 
likened  to  that  of  a  swarm  of  bees  in  a  closed  room, 
when  all  the  bees  are  fly-  Fig  74 

ing  at  random  in  straight 
lines.  They  would  be  con- 
stantly flying  against  each 
other  and  against  the  walls 
of  the  room.  It  has  been 
calculated  that  the  mole- 
cules of  air  are  moving  at 
the  average  rate  of  about 
1600  feet  a  second.  This 
velocity  would  be  sufficient 
to  carry  a  body  in  a  vacuum  some  40,000  feet,  or  about  7 
miles  high.  Now  the  molecules  of  air  in  the  rubber  bag  are 
all  the  time  flying  against  each  other  and  against  the  bag 
with  this  enormous  velocity.  They  therefore  tend  to  expand 
the  bag.  So  long  as  there  was  air  in  the  receiver  outside 
the  bag,  the  blows  against  the  bag  from  within  were  met 
and  balanced  by  an  equal  number  of  blows  from  without ; 
but  as  the  air  was  exhausted  from  the  receiver,  there  were 
fewer  and  fewer  blows  upon  the  bag  delivered  by  the  mole- 
cules on  the  outside,  and  hence  the  bag  began  to  yield  to 
the  more  numerous  blows  from  within. 

1 1 6.  The  Diffusion  of  Gases.  —  When  any  two  gases  are 
brought  into  contact,  they  rapidly  mix  with   each   other. 
This  mixture  of  gases  when  brought  into  contact  is  called 
diffusion.     This  rapid  diffusion  of  gases  is  due  to  the  fact 
that  the  molecules  are  far  apart  and  in  constant  motion. 
The  molecules  of  the  one  gas  quickly  move  into  the  spaces 
among  the  molecules  of  the  other  gas. 

117.  The  Expansive  Power  of  a  Gas  increased  by  Heat.  — 
A  bulb  with  a  tube  projecting  from  it  is  placed  in  a  vessel 
of  water  so  that  the  open  end  of  the  tube  is  under  water,  as 
shown  in  Figure  75.    If  the  bulb  is  heated,  the  air  in  it  will 


84  NATURAL    PHILOSOPHY. 

expand  so  as  to  drive  out  a  portion  of  it  through  the  water. 
Heat   always   increases   the   expansive  power  of    a   gas. 
Fig  75-  This  is  because  heat  causes  the  mole- 

cules to  fly  about  with  greater  velocity, 
and  therefore  with  greater  energy. 

1 1 8.  The  Expansive  Power  of  a  Gas 
increased  by  an  Increase  of  Pressure.  — 
An  increase  of  pressure  on  a  gas  in- 
creases its  expansive  power.  This  is 
because  the  increased  pressure  crowds 
the  molecules  nearer  together,  so  that 
there  are  more  molecules  in  the  same  space  to  beat 
against  the  inclosure.  In  the  cylinder  of  the  steam-engine, 
the  steam  is  kept  at  a  high  temperature  and  under  great 
pressure. 

119.  The  Three  Gaseous  Laws.  —  Equal  volumes  of  all 
gases,  at  the  same  temperature  and  under  the  same  pressure,  con- 
tain the  same  number  of  molecules.  This  is  Avogadrd's  law. 

The  volume  of  a  confined  mass  of  gas  varies  inversely  as  the 
pressure  to  which  it  is  exposed.  The  less  the  pressure  the  greater 
the  volume,  and  the  greater  the  pressure  the  less  the  volume. 
This  is  Mariotte's  law.  This  law  might  be  stated  thus  : 
the  number  of  molecules  of  a  gas  in  a  given  space,  and  the 
expansive  power  of  the  gas,  vary  directly  as  the  pressure  to 
which  the  gas  is  exposed. 

The  volume  of  a  gas  under  constant  pressure  varies  directly 
as  the  absolute  temperature  of  the  gas.  This  is  Charles's  law. 
By  absolute  temperature  is  meant  temperature  measured 
from  a  point  459°  below  the  ordinary  zero.  The  tempera- 
ture indicated  by  an  ordinary  thermometer  may  be  con- 
verted into  absolute  temperature  by  adding  459°  to  it. 
Thus,  a  temperature  of  70°  on  our  scale  would  be  a 
temperature  of  70°  -f-  459°  =  529°  on  the  absolute  scale. 
A  temperature  of  —  15°  on  our  scale  would  be  a  tempera- 
ture of  459°  -j-  (—  15°)  =444°  on  the  absolute  scale. 


NATURAL    PHILOSOPHY.  85 

120.   The  Air-Pump. — The  essential  parts  of   an  air- 
pump  are  shown  in  Figures  76  and  77.     There  is  a  flat 

Fig.  76. 


plate  for  holding  the  receiver  E,  called  the  pump-plate.    It 
is  ground  perfectly  flat,  so  that  an  air-tight  joint  is  formed 

Fig.  77- 


between  it  and  the  receiver  when  the  latter  is  placed  upon 
it.  A  tube  connects  the  pump-plate  with  the  cylinder,  in 
which  a  piston  is  moved  up  and  down  by  means  or  the 


86  NATURAL    PHILOSOPHY. 

handle.  There  is  a  little  valve  .S1  in  the  piston,  pressed  down 
by  a  little  spiral  spring  above  it.  There  is  also  a  valve  S' 
at  the  bottom  of  the  barrel,  fastened  to  a  rod  which 
passes  through  the  piston  in  such  a  way  that  the  valve  is 
opened  when  the  piston  rises,  and  closed  when  the  piston 
is  pushed  down,  by  the  friction  of  the  rod  against  the  pis- 
ton. When  the  piston  is  drawn  up  the  valve  in  the  piston 
is  closed,  and  no  air  can  pass  from  above  the  piston  into 
the  space  below  it.  At  the  same  time  S'  at  the  bottom  of 
the  barrel  is  opened,  and  the  expansive  force  of  the  air  in 
the  receiver  E  causes  some  of  the  air  to  pass  out  through 
the  tube  into  the  barrel  below  the  piston.  On  pushing 
down  the  piston  the  valve  S'  is  closed  by  the  friction  of 
the  rod,  and  the  valve  S  is  opened  by  the  expansive  force 
of  the  air  below  it  as  the  air  becomes  compressed,  and  the 
air  in  the  barrel  below  the  piston  passes  above  it  again.  In 
this  way,  every  time  the  piston  is  moved  up  and  down,  a 
part  of  the  air  is  removed  from  the  receiver.  F  is  a  gauge 
for  showing  the  extent  of  the  exhaustion  ;  I?  is  a  cock,  by 
means  of  which  the  receiver  and  the  barrel  maybe  put  into 
communication  with  each  other,  or  either  may  be  shut  off 
from  the  other  and  be  put  into  communication  with  the 
external  air.  There  is  one  opening  straight  through  this 
cock,  by  means  of  which  the  receiver  and  barrel  may  be 
put  into  communication  with  each  other,  as  shown  in  the 
lower  part  of  Figure  77.  There  is  another  opening  O,  90° 
from  the  former  one,  and  communicating  with  the  external 
air.  When  the  cock  is  turned  so  that  O  is  on  the  side  of 
the  receiver  it  will  put  it  into  communication  with  the  exter- 
nal air  ;  when  O  is  turned  so  as  to  connect  with  the  tube 
on  the  side  of  the  barrel,  it  puts  the  barrel  in  communica- 
tion with  the  external  air. 

There  are  many  different  forms  of  air-pumps  ;  but  with 
none  of  the  ordinary  pumps  is  it  possible  to  obtain  per- 
fect exhaustion.  The  air  becomes  finally  so  attenuated 


NATURAL    PHILOSOPHY. 


as    not  to 
valve. 


have   sufficient   expansive   force   to   open    the 


121.  Sprengefs  Air-Piimp.  —  When  it  is  necessary  to  obtain 
a  more  perfect  exhaustion  than  can  be  obtained  by  an  ordinary 
air-pump,  some  form  of  a  mercurial  Fig.  78. 

pump  is  employed.  Figure  78  shows 
the  simplest  form  of  Sprengel's 
air-pump,  and  serves  to  illustrate 
the  principle  of  all  these  mercu- 
rial air-pumps.  An  upright  tube 
cd,  some  four  or  five  feet  in  length, 
is  connected  at  c  by  a  short  piece  of 
rubber  tubing  to  a  funnel  A,  filled 
with  mercury.  The  rubber  tubing 
at  c  may  be  closed  by  means  of  a 
clamp,  when  the  pump  is  not  in 
operation.  The  bottom  of  the  tube 
passes  into  a  vessel  £,  into  which 
it  is  fastened  by  a  cork.  The 
vessel  B  has  a  spout  at  the  side, 
just  a  little  above  the  lower  end  of 
the  upright  tube.  The  upright  tube 
has  a  branch  at  x,  by  means  of 
which  it  is  connected  with  the  re- 
ceiver y?,  from  which  the  air  is  to  be  exhausted.  The  mercury, 
being  allowed  to  fall  through  the  upright  tube,  carries  by  fric- 
tion some  of  the  air  from  the  tube  x  down  with  it.  The  ex- 
pansion of  the  air  in  the  receiver  brings  fresh  air  into  the  tube 
as  fast  as  it  is  removed  by  the  falling  mercury.  The  whole 
length  of  the  tube  from  x  down  becomes  filled  with  cylinders  of 
mercury,  separated  by  cylinders  of  air,  all  moving  downward. 
The  air  and  mercury  escape  from  the  spout  at  the  side  of  the 
vessel  B,  and  the  mercury  is  caught  in  a  basin,  and  from  time 
to  time  poured  back  into  the  funnel  A.  As  the  exhaustion 
progresses,  the  air  enclosed  between  the  cylinders  of  mercury 
becomes  less  and  less,  and  finally  disappears  entirely. 

Sprengel's  pump  is  only  one  of  the  many  applications  of  the 
aspiratory  effects  of  a  current  of  air  or  of  a  liquid.  Whenever 


* 


88 


NATURAL    PHILOSOPHY. 


a  current  of  air  or  of  liquid  passes  through  a  gas,  it  carries  some 
of  the  surrounding  gas  along  with  it,  and  so  produces  a  partial 
exhaustion  in  its  neighborhood,  which  occasions  an  inflow  from 
all  sides. 

122.  Pressure  of  the  Air.  —  The  pressure  of  the  air  may 
be  illustrated  by  the  following  experiments.  Place  a  small 
bell-jar,  open  at  both  ends,  on  the  plate  of  the  air-pump, 
and  cover  the  top  of  the  jar  with  the  palm  of  the  hand. 
When  the  air  is  exhausted  from  the  jar,  the  hand  is  pressed 
firmly  down  upon  the  mouth  of  the  jar.  This  is  an  illus- 
tration of  the  downward  pressure  of  the  air.  It  was  not 
perceived  at  first,  because  the  downward  pressure  of  the 
air  upon  the  hand  was  balanced  by  the  upward  pressure  of 
the  air  within  the  jar. 

The  weight-lifter  (Figure  79)  serves  to  illustrate  the  up- 
ward pressure  of  the  air.  It  consists  of  a  cylinder  of  glass 
or  metal,  A  B,  with  a  piston 
moving  up  and  down  in  it,  air- 
tight. This  cylinder  is  closed  at 
the  top  by  a  plate  C,  to  which 
may  be  screwed  a  tube  to  con- 
nect the  cylinder  with  the  air- 
pump.  The  cylinder  is  open  at 
the  bottom,  and  a  heavy  weight 
is  fastened  with  a  strap  to  the 
piston.  If  the  air  is  exhausted 
from  the  cylinder  above  the  pis- 
ton, the  piston  and  weight  are 
raised  by  the  upward  pressure 
of  the  air  acting  upon  the  bot- 
tom of  the  piston. 
Figures  80  and  81  represent  two  brass  hemispheres, 
some  four  inches  in  diameter,  the  edges  of  which  are  made 
to  fit  tightly  together.  The  whole  can  be  screwed  to 
the  air-pump  by  means  of  the  stop-cock  at  the  bottom. 


NATURAL   PHILOSOPHY.  89 

While  the  hemispheres  contain  air  they  can  be  separated 
Fig.  80.  with  ease,  since  the  out-         Fig.  gi. 

ward  pressure  is  just  bal- 
anced    by    the      inward 

pressure;    but  when   the 

air  within  is  pumped  out, 

it   is   very   hard   to    pull 

them  apart.     Since  it   is 

equally  difficult  to  do  this 

in  whatever  position  the 

hemispheres  are  held,  the 

experiment     shows     that 

the  air  presses  in  all  di- 
rections. 

This  piece  of  apparatus 

is  called  the  Magdeburg 
hemispheres,  from  Otto  von  Guericke,  of 
Magdeburg,  by  whom  it  was  invented. 

The  pressure  of  the  air  at  the  level  of  the  sea  is  about 
15  pounds  to  a  square  inch,  or  a  ton  to  the  square 
foot. 

The  surface  of  the  body  of  a  man  of  middle  size  is 
about  1 6  square  feet ;  the  pressure,  therefore,  which  a  man 
supports  on  the  surface  of  his  body  is  35,560  pounds,  or 
nearly  16  tons.  Such  enormous  pressure  might  seem  im- 
possible to  be-  borne ;  but  it  must  be  remembered  that,  in 
all  directions,  there  are  equal  and  contrary  pressures  which 
counterbalance  one  another.  It  might  also  be  supposed 
that  the  effect  of  this  force,  acting  in  all  directions,  would 
be  to  press  the  body  together  and  crush  it.  But  the  solid 
parts  of  the  skeleton  could  resist  a  far  greater  pressure ; 
and  the  cavities  of  the  body  are  filled  with  air  or  liquids 
which  exert  a  pressure  outward  equal  to  that  of  the  ex- 
ternal air.  When  the  external  pressure  is  removed  from 
any  part  of  the  body,  either  by  means  of  a  cupping  vessel 


9o 


NATURAL   PHILOSOPHY. 


or  by  the  air-pump,  the  pressure  from  within  is  seen  by  the 
distension  of  the  surface. 

123.  The  Pressure  of  the  Air  decreases  as  we  ascend  above 
the  Level  of  the  Sea.  —  The  pressure  of  the  air  at  the  level 
of  the  sea  is  due  to  the  downward  pressure  of  all  the  layers 
of  air  above,  transmitted  throughout  the  mass  below  ac- 
cording to  Pascal's  law.     Each  layer  of  molecules  of  air  is 
pulled  downward  by  gravity,  and  transmits  this  pressure  to 
all  the  layers  below.      Hence  the  pressure  of  a  gas  in- 
creases with  the  depth.     It,  however,  increases  more  rap- 
idly than  the  depth.     For  gases  being  compressible,  as  we 
descend  in  a  gas  the  molecules  are  crowded  more  closely 
together,  so  that  there  are  more  molecules  exerting  pres- 
sure in  each  layer,  and  there  are  more  layers  in  any  given 
difference  of  depth. 

D.   LIQUIDS. 

124.  Compressibility  of  Liquids. — For  a  long  time  it 
was  thought  that  liquids  were  entirely  incompressible.     In 

the  year  1661  some  academicians  of 
Florence,  wishing  to  find  whether  water 
was  compressible,  filled  a  thin  globe  of 
gold  with  that  liquid,  and,  after  closing 
the  orifice  perfectly  tight,  subjected 
the  globe  to  great  pressure,  with  a 
view  of  altering  its  form,  knowing  that 
any  alteration  of  form  would  occasion 
a  diminution  of  capacity.  They  failed 
to  compress  the  water,  but  discovered 
the  porosity  of  gold,  for  the  water 
forced  its  way  through  the  pores  of 
the  globe,  and  stood  on  the  outside 
like  dew. 

In  more  recent  times  it  has  been  shown 
that  liquids  are  slightly  compressible. 
The  apparatus  for  measuring  the  com- 


NATURAL   PHILOSOPHY.  91 

pressibility  of  a  liquid  is  shown  in  Figure  82.  It  consists  of  a 
strong  glass  cylinder  within  which  there  is  a  long  glass  bulb  A, 
from  which  proceeds  a  fine  bent  tube,  with  its  end  dipping 
under  the  mercury  in  the  bottom  of  the  cylinder  at  O.  The 
liquid  to  be  tested  is  introduced  into  the  bulb  A  so  as  to  fill 
both  it  and  the  tube.  The  cylinder  is  then  filled  with  water 
through  the  funnel  /?,  and  pressure  applied  by  means  of  the 
thumb-screw  /*,  which  forces  a  piston  down  upon  the  water. 
The  rise  of  the  mercury  in  the  fine  tube  shows  the  amount 
of  the  compression  of  the  liquid  in  the  bulb.  For  a  pressure 
of  one  atmosphere,  or  15  pounds  to  the  square  inch,  the  volume 
of  water  is  diminished  about  5  parts  in  100,000.  At  the  depth  of 
a  mile,  the  volume  of  sea-water  is  diminished  i  part  in  130. 

In  liquids,  as  in  gases,  elasticity  is  developed  only  by 
compression,  but  their  elasticity  is  perfect.  No  matter  to 
what  pressure  a  liquid  has  been  subjected,  it  will  return 
to  exactly  its  original  volume  as  soon  as  the  pressure  is 
removed. 

125.  The  Tendency  of  Liquids  to  assume  a  Globular 
Form.  —  When  left  to  itself,  a  liquid  always  assumes  a 
globular  form.  This  is  because  all  the  molecules,  as  they 
work  their  way  through  the  mass,  are  stopped  by  the  force 
of  gravity  and  cohesion  at  the  same  distance  from  the 
centre  of  the  mass.  The  tendency  of  the  molecules  of 
liquids  to  collect  into  spheres  may  be  shown  by  the  follow- 
ing experiment.  Prepare  a  mixture  of  water  and  alcohol 
which  shall  be  just  as  heavy  as  sweet-oil,  bulk  for  bulk, 
and  introduce  some  of  the  oil  carefully  into  the  centre  of 
this  mixture  by  means  of  a  dropping-tube  ;  the  oil  will 
neither  rise  nor  sink,  but  gather  into  a  beautiful  sphere. 

Rain-drops,  dew-drops,  and  the  manufacture  of  shot 
illustrate  this  tendency  of  the  molecules  of  liquids.  In 
the  manufacture  of  shot,  melted  lead  is  poured  through  a 
sieve  at  the  top  of  a  very  high  tower,  and  the  drops  in 
falling  take  the  form  of  spheres,  which  become  solid  before 
they  reach  the  bottom. 


92  NATURAL    PHILOSOPHY. 

126.  The  Free  Surface  of  a  Liquid  at  Rest  is  a  Level 
Surface.  —  A  level  surface  is  one  along  which  gravity  does 
not  tend  to  produce  any  motion.     Gravity  always  acts  per- 
pendicularly to  such  a  surface,  and  hence  there  can  be  no 
component  of  gravity  which  would  tend  to  produce  motion 
along  that  surface. 

The  surface  of  a  liquid  at  rest  must  be  a  level  surface, 
else  gravity  would  tend  to  move  the  liquid  along  the  sur- 
face, and  the  liquid  could  not  remain  at  rest. 

Thus,  in  Figure  83,  if  the  surface  of  the  liquid  were  not  level, 
Pig  83  the  force  of  gravity  acting  upon  the  par- 

ticle M  would  be  decomposed  into  two 
components,  —  one  perpendicular  t6  the 
surface  which  would  produce  pressure, 
and  one  along  the  surface  which  would 
produce  motion. 

127.  The  Downward  Pressure  of  a  Liquid  due  to  Gravity 
is  proportional  to  the  Depth.  —  Since  the  downward  pres- 
sure of  a  liquid  due  to  gravity  at  any  point  is  the  pressure 
that  has  been  transmitted  to  that  point  by  the  layers  of 
molecules  above,  the  pressure  at  that  point  will  be  propor- 
tional   to   the  number  of  layers  of  molecules   above  the 
point; -and  since   liquids  are   practically  incompressible, 
the  number  of  layers  of  molecules  will  be  proportional    to 
the  depth. 

The  amount  of  pressure  transmitted  to  the  layers  below 
by  any  layer  of  molecules  is  entirely  independent  of  the 
extent  of  the  layer.  For  if  the  upper  layer  consisted  of  a 
single  molecule,  it  would  exert  the  pressure  of  a  molecule 
upon  the  surface  of  a  molecule,  and  that  pressure  would 
be  transmitted  to  every  equal  surface  below.  If  the  upper 
layer  consisted  of  5  molecules,  they  would  exert  a  pressure 
of  5  molecules  upon  a  surface  of  5  molecules,  which  would 
be  the  pressure  of  one  molecule  to  the  surface  of  one 
molecule  as  before.  Hence  the  pressure  at  any  point  in  a 


NATURAL    PHILOSOPHY. 


93 


vessel  containing  a  liquid  does  not  depend  at  all  upon  the 
size  and  shape  of  the  vessel,  but  simply  upon  the  depth  of 
the  point  below  the  surface. 

128.  PascaFs  Vases. — The  fact  that  the  pressure  of  a 
liquid  upon  a  given  surface  depends  upon  the  depth  of  the 
liquid  only,  and  not  upon  the  size  or  shape  of  the^ vessel 
which  contains  the  liquid,  may  be  illustrated  by  means  of 
Pascal's  vases  (Figure  84).  The  vessels  M,  P,  and  Q  may 
in  turn  be  screwed  into  the  plate  c.  A  disc  a  suspended 
from  one  end  of  the  beam  of  a  balance  with  a  thread,  and 

Fig.  84. 


held  up  by  weights  at  the  other  end  of  the  beam,  serves 
as  the  bottom  of  the  vessel,  which  it  closes  water-tight. 
Water  is  poured  carefully  into  the  vessel  M  \\\\  its  depth 
is  just  sufficient  to  displace  the  plate  a,  and  the  height  of 
the  water  is  marked  by  the  point  o.  J/is  then  removed, 
and  P  and  Q  are  in  turn  put  into  its  place.  It  will  be 
found  that  each  will  have  to  be  filled  to  exactly  the  same 
height  to  displace  the  plate  a. 

It  follows  from  the  above  that  a  very  small  quantity  of 
water  can  produce  considerable  pressure.  Let  us  ima- 
gine a  cask,  for  example,  filled  with  water,  and  having  a 
long  narrow  tube  tightly  fitted  into  its  top.  If  water 


94  NATURAL    PHILOSOPHY. 

is  poured  into  the  tube,  there  will  be  a  pressure  on  the 
bottom  of  the  cask  equal  to  the  weight  of  a  column  of 
water  whose  base  is  the  bottom  itself,  and  whose  height  is 
equaPto  that  of  the  water  in  the  tube.  The  pressure  may 
be  made  as  great  as  we  please  ;  by  means  of  a  mere 
thread  of  water  forty  feet  high,  Pascal  succeeded  in  burst- 
ing a  very  solidly  constructed  cask. 

129.  The   Upward  Pressure  of  a  Liquid.  —  The  down- 
ward pressure  of  a  liquid  at  any  point  must  be  balanced 
by  an  equal  upward  pressure,  according  to  the  law  that 
action  and  reaction  are  always  equal  and  opposite. 

The  following  experiment  (Figure  85)   serves  to  show 
the  upward  pressure  of  liquids.     A  large  open  glass  tube 
Fig.  85.  A,  one  end  of  which  is  ground,  is  fitted 

with  a  ground-glass  disc  O,  or  still  bet- 
ter with  a  thin  card  or  piece  of  mica,  the 
weight  of  which  may  be  neglected.  To 
this  is  attached  a  string  C,  by  which  it 
can  be  held  against  the  bottom  of  the 

tube.     If   the    whole   is    then    immersed 

•^gj  f§jj9fe  *n  wa-ter,  the  disc  does  not  fall,  al- 
though no  longer  held  by  the  string  ;  it 
is  consequently  kept  in  its  position  by  the  upward  pressure 
of  the  water.  If  water  is  now  slowly  poured  into  the 
tube,  the  disc  will  sink  only  when  the  height  of  the  water 
inside  the  tube  is  equal  to  the  height  outside. 

130.  The  Pressures  of  different  Liquids  at  the  same  DeptJi 
are  proportional  to  their  Densities.  —  The  pressure  at  the 
same  depth  would  be  about  12^  times  as  great  in  mercury 
as  in  water,  and  about  .8  as  great  in  alcohol  as  in  water. 
This  is  owing  to  the  fact  that,  mercury  being  about  iz}/> 
times  as   dense   as  water,   each  layer  of  mercury  would 
transmit  downward  12^2  times  as  much  pressure  as  a  layer 
of  the  same  thickness  of  water ;  and  a  layer  of  alcohol, 
.8  times  as  much. 


NATURAL    PHILOSOPHY. 


95 


131.  The  Pressure  is  the  same  at  every  Point  in  a  Hori- 
zontal Layer  of  a  Liquid  at  Rest.  —  Owing  to  the  extreme 
mobility  of  liquids,  it  would  be  impossible  for  a  liquid  to 
remain  at  rest  if  at  any  point  in  it  the  pressures  acting 
upon  that  point  from  all  directions  were  not  equal  or  bal- 
anced.    If  the  upward  or  downward  pressure  at  any  point 
were  not  balanced,  a  particle  at  that  point  would  tend  to 
move  up  or  down  as  the  case  might  be.     If  the  pressure 
were  not  the  same  throughout  a  horizontal  layer,  there 
would  be  some  point  in  the  horizontal  layer  where  the 
horizontal   pressures  to  the  right  and   left  would  not  be 
balanced,  and  a  particle  at  that  point  would  move  in  the 
direction   in  which   it  was  urged  by  the  larger  pressure  ; 
that  is,  the  liquid  would  not  be  at  rest.      This  is  true  of 
all  fluids,  both  liquids  and  gases. 

Any  disturbance  of  the  equilibrium  of  pressure  in  hori- 
zontal layers  gives  rise  to  currents  which  will  flow  towards 
the  region  of  low  pressure  till  the  equilibrium  is  restored. 

132.  Rise  of  Liquids  in  Communicating  Vessels.  —  When 
a  liquid  is  contained  in  vessels  which  communicate  with  each 


Fig.  86. 


other  and  is   at   rest,   it 

will  be  found  to  stand  at 

the   same   height   in    all 

the  vessels,  whatever  may 

be   their   size   or   shape. 

Thus,  in   Figure  86    the 

water  stands  at  the  same 

height  in  all  the  tubes  as 

in  the   large  vessel.      If 

one  of  the   tubes  is  cut 

off  below  the  level  of  the 

water  in   the  other  vessels,  and  drawn   out   to  a  narrow 

mouth,  the  liquid  will  spout  out  of  this  tube  nearly  to  the 

height  of  the  liquid  in  the  others.     The  rise  of  a  liquid 

to  the  same  height  in  a  series  of  communicating  vessels  is 


96 


NATURAL    PHILOSOPHY. 


due  to  the  fact  that  when  a  liquid  is  at  rest,  the  pressure 
must  be  the  same  throughout  each  horizontal  layer.  Each 
horizontal  layer  of  the  water  taken  through  all  the  vessels 
must  then  be  the  same  distance  below  the  free  surface  of 
the  liquid  in  each  vessel.  Hence  these  free  surfaces  must 
be  in  the  same  horizontal  line,  or  at  the  same  level. 

The  tendency  of  liquids  to  find  their  own  level  is  very 
important,  and  of  continual  application.  When  any  sys- 
tem of  pipes,  however  complicated,  is  connected  with  a 
reservoir,  the  water  will  rise  in  every  pipe  to  the  level  of 
the  water  in  the  reservoir. 

Fig.  87. 


133.  Springs  and  Artesian  Wells.  —  All  natural  collec- 
tions of  water  illustrate  the  tendency  of  a  liquid  to  find  its 
level.  Thus,  the  Great  Lakes  of  North  America  may  be 
regarded  as  a  number  of  vessels  connected  together,  and 
hence  the  waters  tend  to  maintain  the  same  level  in  all. 
The  same  is  true  of  the  source  of  a  river  and  the  sea,  the 
bed  of  the  river  connecting  the  two  like  a  pipe. 

Springs  illustrate  the  same  fact.  The  earth  is  composed 
of  layers,  or  strata,  of  two  kinds  :  those  through  which 
water  can  pass,  as  sand  and  gravel ;  and  those  through 
which  it  cannot  pass,  as  clay.  The  rain  which  falls  on 
high  ground  sinks  through  the  soil  until  it  reaches  a  layer 
of  this  latter  kind,  and  along  this  it  runs  until  it  finds 
some  opening  through  which  it  flows  as  a  spring. 


NATURAL    PHILOSOPHY.  97 

It  is  the  same  with  Artesian  wells.  These  wells  derive 
their  name  from  the  province  of  Artois  in  France,  the  first 
part  of  Europe  where  they  became  common.  It  would 
seem,  however,  that  wells  of  the  same  kind  were  made  in 
China  and  Egypt,  many  centuries  earlier. 

In  Figure  87,  suppose  A  B  and  CD  to  be  two  strata  of 
clay,  and  K  K to  be  a  stratum  of  sand  or  gravel  between 
them.  The  rain  falling  on  the  hills  on  either  side  will 
filter  down  through  this  sand  or  gravel,  and  collect  in  the 
hollow  between  the  two  strata  of  clay,  which  prevent  its 
escape.  If  now  a  hole  is  bored  down  to  K  K,  the  water, 
striving  to  regain  its  level,  will  rise  to  the  surface  at  H,  or 
spout  out  to  a  considerable  height  above  it. 

Sometimes  the  water  between  two  such  impervious  strata 
makes  its  way  to  the  surface  through  some  fissure  in  the 
upper  stratum,  constituting  a  deep-seated  spring. 

Fig.  83. 


134.  The    Water-Level.  —  The   water-level    (Figure    88)    is 
constructed  on   the  principle  that  water  will   rise  to  the  same 
level   in   two   communicating  vessels.     It   consists   of  a  metal 
tube  b  bent  at  right  angles  at  its  extremities.     It  carries  at  each 
end  a  glass  tube  a  of  the  same  size.     The  tube  is  supported  on 
a  tripod  stand.     It  is  first  placed  in  a  nearly  horizontal  position, 
and  then  some  colored  water  is  poured  into  the  glass  tube  a. 
The  water  rises  to  the  same  level  in  both  the  glass  tubes.     The 
line  of  sight  m  n,  which  just  grazes  the  two  surfaces,  will  be  a 
horizontal  line. 

135.  The    Spirit-Level — The    operations    of    levelling    are 


98 


NATURAL   PHILOSOPHY. 


effected  much  more  easily  and  accurately  by  means  of  an  in- 
strument called  the  spirit-level. 

It  consists  of  a  closed  glass  tube,  A  B  (Figure  89),  with  a 

slight  upward  curvature.     It  is  filled  with  spirit,  except  a  bubble 

Fig.  89.  of  air  which  tends  to  rise 

cS"'B<^l_       ^        ~^ -»=^" •      to  the  highest  part  of  the 

^^piE  ^A     p    tube.     It  is  set  in  a  case 

CD,    and   when    this   is 

placed  on  a  perfectly  level  surface,  the  bubble  is  exactly  in  the 
middle  of  the  tube,  as  in  the  figure. 

136.   Rise  of  two  Different  Liquids  in  Communicating  Ves- 
sels.—  If  into  one  of  two  communicating  tubes  (Figure  90) 
F'g-  90  we  pour  any  liquid,  as 

mercury^  it  will  rise  to 
the  same  height  in  both 
branches.  If  now  we 
pour  water  into  one  of 
the  tubes,  the  mercury 
will  rise  somewhat  in 
the  other,  but  not 
nearly  so  high  as  the 
water.  The  heiglit  of 
the  two  liquids  above 
the  surface  of  separa- 
tion will  be  in  the 
inverse  ratio  of  the 
densities  of  the  liquids.  This  will  be  true  in  all  cases.  This 
is  because  the  pressures  of  the  two  liquids  at  the  surface  of 
separation  must  be  equal,  so  as  to  balance  each  other. 
Now  the  downward  pressure  of  the  water  at  the  surface  of 
the  mercury  is  due  to  the  depth  of  the  water  above  it,  and 
the  upward  pressure  of  the  mercury  at  the  same  point  is 
due  to  the  depth  'of  the  mercury  above  the  level  of  this 
surface  in  the  other  tube ;  and  to  have  these  pressures 
equal,  these  depths  must  be  in  the  inverse  ratio  of  the  den- 
sities of  the  liquids. 


NATURAL  PHILOSOPHY. 


99 


137.  Capillarity.  —  The  rise  of  liquids  in  communicat- 
ing vessels  is  modified  in  a  remarkable  manner  when  any 
of  the  communicating  vessels  are  very  narrow.  Such  nar- 
row vessels  and  fine  tubes  are  called  capillary,  from  the 
Latin  capillus,  a  hair.  The  action  of  such  tubes  upon  the 
rise  of  liquids  within  them  is  called  capillary  action.  This 
action  is  not,  however,  confined  to  the  cases  of  fine  tubes ; 
but  when  the  containing  vessel  is  wide,  the  action  extends 
only  a  short  distance  from  the  sides  of  the  vessel.  The 
free  surface  of  a  liquid  in  a  wide  vessel  is  not  horizontal 
in  the  neighborhood  of  the  sides  of  the  vessel,  but  presents 
a  very  decided  curvature.  When  the  liquid  wets  the  vessel, 
as  in  the  case  of  water  in  a  glass  vessel  (Figure  91),  the 


Fig.  91.  Fig.  92. 


Fig.  93-  Fig.  94. 


surface  of  the  liquid  near  the  glass  is  concave.  When  the 
liquid  does  not  wet  the  vessel,  as  in  the  case  of  mercury 
in  a  glass  vessel  (Figure  92),  the  surface  near  the  glass  is 
convex. 

When  a  narrow  tube  of  glass  is  plunged  into  water  or 
any  other  liquid  that  will  wet  it  (Figure  93),  the  liquid 
rises  higher  within  the  tube  than  on  the  outside,  and  the 
column  of  the  liquid  within  the  tube  will  be  concave  at 
the  top.  In  this  case  there  is  a  capillary  ascension  which 
varies  in  amount  with  the  diameter  of  the  tube  and  the 
nature  of  the  liquid.  The  finer  a  tube,  the  higher  the 
liquid  will  rise  in  it.  If  a  glass  tube  is  plunged  in  mer- 
cury, which  does  not  wet  it,  the  mercury  will  fall  within  the 
tube  below  the  level  of  the  mercury  outside  (Figure  94), 


NATURAL  PHILOSOPHY. 


and  the  top  of  the  column  of  mercury  within  the  tube  will 
have  a  convex  surface.  In  this  case  there  is  a  capillary 
depression.  The  finer  the  tube,  the  greater  the  depression. 

If  we  take  two  bent  tubes,  each  having  one  branch  of 
considerable  diameter,   and  the  other  extremely  narrow, 
and  pour  water  into  one  of  the  tubes,  and  mercury  into  the 
other,  the  water  will  stand  higher  in  the  capillary  than  in 
Fig.  95.  the  principal   branch,  and  the  mer- 

cury will  stand  lower  in  the  capillary 
branch  (Figure  95).  The  free  sur- 
face will  be  concave  in  both  branches 
in  the  case  of  water,  and  convex  in 
the  case  of  mercury.  Capillary  ac- 
tion is  manifested  whenever  the  sur- 
face of  a  liquid  comes  in  contact 
with  a  solid.  If  a  clean  glass  plate 
is  dipped  into  water,  the  water  will 
rise  a  little  on  each  side  of  the  plate.  If  the  same  plate 
is  clipped  in  mercury,  the  mercury  will  be  depressed  a 
little  on  each  side  of  the  plate.  Capillary  action  is  also 
often  manifested  when  the  surfaces  of  two  liquids  are 
brought  into  contact  by  the  peculiar  movements  which 
take  place. 

138.  Illustrations  of  Capillarity.  —  A  lamp-wick  is  full  of 
tubes  and  pores,   and   capillary  force  draws    the    oil    up 
through  these  to  the  top  of  the  wick,  where  it  is  burned 
When  one  end  of  a  cloth  is  put  into  water,  capillary  force 
draws  the  water  into  the  tubes  and  pores  of  the  cloth,  and 
the  whole  soon  becomes  wet.     In  the  same  way  any  other 
porous  substance  soon  becomes  wet  throughout,  if  a  corner 
of  it  is  put  into  water.     Blotting-paper  is  full  of  pores  into 
which  the  capillary  force  draws  the  ink.     The  use  of  a 
towel  for  wiping   anything  which  is  wet  depends  on  the 
same  principle. 

139.  Strength  of  the  Capillary  Force.  —  It  is  well  known 


NATURAL   PHILOSOPHY.  IOI 

that  when  a  piece  of  cloth  is  wet,  it  is  almost,  if  not  quite, 
impossible  to  wring  or  squeeze  it  dry.  This  shows  that 
the  capillary  force  which  holds  the  water  in  the  pores  of  the 
cloth  is  very  strong.  Some  solids,  as  wood,  swell  on  becom- 
ing wet.  If  holes  are  drilled  into  a  granite  rock,  and  dry 
wooden  plugs  driven  into  them,  and  water  is  then  poured 
over  the  ends  of  the  plugs,  the  capillary  force  draws  the 
water  into  the  wood,  which  swells  and  splits  the  rock. 
This  is  a  striking  illustration  of  the  strength  of  the  capil- 
lary force. 

140.  Capillary  Force  never  causes  a  Liquid  to  flow  through 
a  Tube.  —  If  a  glass  tube  is  so  fine  that  the  capillary 
force  will  draw  water  into  it  to  the  height  of  two  inches, 
and  the  tube  is  then  lowered  so  that  not  more  than  half 
an  inch  shall  be  above  the  surface  of  the  water,  the  water 
will  not  overflow  the  tube.  If,  however,  the  water  is  re- 
moved as  soon  as  it  comes  to  the  top,  more  will  rise  in  the 
tube  to  take  its  place. 

When  a  lamp  is  burning,  the  oil  is  passing  up  continually 
through  the  wick,  because  it  is  burned  as  soon  as  it  reaches 
the  top ;  but  when  the  lamp  is  not  burning  the  oil  does 
not  overflow  the  wick. 

Fig.  96.  Fig.  97. 


141 .  Heavy  Bodies  floating  on  Water  by  Capillary  Action.  — 
According  to  Archimedes's  principle,  a  body  cannot  float  on  a 
liquid  unless  it  is  less  dense  than  the  liquid.  This  seems  to  be 
contradicted  by  certain  well-known  facts.  Small  steel  needles 
will  float  on  water  when  placed  carefully  on  the  surface  (Fig- 
ure 96).  Several  insects  walk  on  water  (Figure  97),  and  many 


NATURAL    PHILOSOPHY. 


heavy  bodies  can,  if  sufficiently  minute,  float  on  the  surface  of 
water.     In  all  these  cases  the  bodies  are  not  wet  by  the  liquid, 
and  consequently  depressions  are   formed 
around  them  by  capillary  action,  as  shown 
in  Figure  98.     The  liquid  displaced  by  one 
of  these  bodies  is  really  equal  to  that  which 
would  fill  the  whole  depression,  or  the  space 
below  the  dotted  line  CD  (Figure  98),  and 
this  liquid  would  in  every  case  be  equal  to 
the  weight  of  the  floating  body. 

142.    Endosmose. —  If  a  vessel  v  (Figure  99),  closed  below 
by  a  thin  membrane  b  a,  and  terminating  above  in  a  long  tube, 
Fig  99.  is  filled  with  a  solution  of  gum  in  water,  and 

immersed  in  water,  the  liquid  will  slowly  rise 
in  the  tube  till  it  reaches  a  certain  point  n. 
At  the  same  time  traces  of  gum  will  be  found 
in  the  water  outside.  The  water  passes  in 
through  the  membrane  and  mixes  with  the  so- 
lution on  the  inside,  while  some  of  the  gum 
passes  out  through  the  membrane  and  mingles 
with  the  water  outside.  The  rise  of  the  liquid 
in  the  tube  shows  that  the  water  passes  in 
faster  than  the  gum  passes  out.  Similar  results 
would  be  obtained  if  water  holding  albumen, 
sugar,  or  gelatine  in  solution  were  employed  in 
the  small  vessel,  or  if  the  membrane  were  re- 
placed by  a  slab  of  wood  or  porous  clay.  The 
passage  of  two  liquids  through  a  membrane 
or  porous  substance  which  separates  them  is  called  endosmosc. 
There  are  two  currents  of  different  volumes  which  flow,  through 
the  membrane  in  opposite  directions.  Sometimes  the  term  en- 
dosmose  is  applied  to  the  more  abundant  flow,  and  the  term  exos- 
mose  to  the  less  abundant  flow.  The  phenomena  of  endosmose 
are  somewhat  akin  to  those  of  capillarity. 

Substances  have  been  divided  into  two  classes  as  regards 
their  power  of  passing  through  porous  diaphragms,  namely,  into 
crystalloids  and  colloids.  The  former  are  susceptible  of  crystal- 
lization, form  solutions  free  from  viscosity,  are  sapid,  and  have 
great  powers  of  diffusion  through  porous  septa.  The  latter, 


NATURAL   PHILOSOPHY.  103 

including  gum,  starch,  albumen,  etc.,  are  characterized  by  a 
remarkable  sluggishness  and  indisposition  both  to  diffusion  and 
to  crystallization,  and  when  pure  are  nearly  tasteless. 

143.  Rise  of  Liquids  in  Exhausted  Tubes. —  Since  the 
atmosphere  presses  15  pounds  to  the  square  inch  upon  the 
surface  of  a  liquid,  if  this  pressure  is  removed  or  lessened 
at  any  point  on  the  surface,  the  liquid  will  tend  to  rise  at 
that  point.  If  a  long  glass  tube,  open  at  both  ends,  is 
connected  at  the  top  by  means  of  a  rubber  tube  with  an 
air-pump,  and  is  held  upright  with  its  lower  end  under 
the  surface  of  mercury,  when  the  pump  is  worked  the  mer- 
cury .will  begin  to  rise  in  the  tube,  and  it  will  rise  higher 
and  higher  as  the  exhaustion  continues.  Were  a  tube  over 
30  inches  long  connected  with  a  Sprengel  air-pump  so  as  to 
secure  a  more  perfect  exhaustion,  the  mercury  would  rise 
about  30  inches  in  the  tube.  Under  similar  circumstances 
water  would  rise  about  33  feet  high.  In  each  case  the 
liquid  would  rise  in  the  tube  till  the  pressure  within  the 
tube  at  a  level  with  the  surface  of  the  liquid  outside  was 
equal  to  the  pressure  of  the  air  on  the  surface  of  the 
liquid,  or  about  15  pounds  to  the  square  inch.  The 
height  to  which  different  liquids  will  rise  in  exhausted 
tubes  will '  be  in  the  inverse  ratio  of  the  densities  of  the 
liquids. 

In  drinking  lemonade  through  a  straw,  the  air  is  first 
drawn  out  of  the  straw  by  the  mouth,  and  the  liquid  is 
forced  up  through  the  straw  by  the  pressure  of  air  on  the 
surface.  When  a  jar  is  filled  with  a  liquid  and  then 
inverted  with  its  mouth  under  the  same  liquid  in  a 
vessel,  the  pressure  of  the  air  on  the  surface  of  the  liquid 
in  the  vessel  will  keep  the  liquid  up  in  the  jar. 

That  it  is  the  pressure  of  the  atmosphere  on  the  surface 
of  the  liquid  in  the  vessel  that  keeps  the  liquid  up  in  the 
jar  may  be  shown  by  the  following  experiment.  Fill  a  jar 
with  mercury,  invert  it,  and  place  its  mouth  under  some 


104 


NATURAL   PHILOSOPHY. 


mercury  in  a  dish.  Place  the  jar  thus  inverted  in  the  dish 
of  mercury  under  the  receiver  of  an  air-pump,  and  exhaust 
the  air.  As  the  exhaustion  proceeds,  and  the  pressure  of 
the  air  upon  the  surface  of  the  mercury  becomes  less  and 
less,  the  mercury  falls  in  the  jar. 

144.    The   fountain   in    Vacuo.      This   apparatus   is    an 
illustration  of  the  tendency  of  liquids  to  rise  in  exhausted 

Fig.  ioo. 


vessels  (Figure  ioo).  It  consists  of  a  bell-jar,  provided  with 
a  tube  and  stopcock  at  the  bottom.  The  bell-jar  is  first 
exhausted  by  means  of  the  air-pump.  The  stopcock  is  then 
closed,  and  the  bell-jar  is  removed  to  a  vessel  of  water. 
After  the  end  of  the  tube  has  been  placed  under  water  the 
stopcock  is  again  opened.  The  pressure  of  the  air  on  the 
surface  of  the  water  in  the  vessel  drives  the  water  up  in 
the  bell-jar  in  a  jet  so  as  to  form  a  beautiful  fountain. 

145.  Torricellfs  Experiment.  —  Torricelli  took  a  glass 
tube  somewhat  more  than  30  inches  long  and  closed  at 
one  end,  and  filled  it  with  mercury.  He  then  closed  the 
tube  with  his  thumb,  and  inverted  it  in  a  dish  of  mercury 
(Figure  101).  On  opening  the  tube  under  the  mercury, 


NATURAL    PHILOSOPHY. 


he  found  that  the  mercury  Fig.  101. 

fell  in  the  tube  till  the  top 
of  the  column  A  stood  about 
30  inches  above  the  surface 
of  the  mercury  in  the  dish. 
Such  a  tube  is  called  a  Tor- 
ricellian tube,  and  the  space 
above  the  column  of  mer- 
cury in  the  tube  is  called  a 
Torricellian  vacuum. 

146.  Pascal's  Experiment. 
—  Pascal  had  a  Torricellian 
tube  taken  from  the  bottom 
to   the   top  of   a  mountain, 
and  ascertained  that  the  col- 
umn of  mercury  in  the  tube 
fell  as  the  ascent  progressed. 
He  therefore  concluded  that 
the  mercury  was  kept  up  in 
the  tube  by  the  pressure  of 
the  atmosphere  on  the  sur- 
face of  the  mercury  in  the 
vessel,    since    the    pressure 

would  necessarily  become  less  and  less  as  we  ascend  from 
the  level  of  the  sea. 

147.  The  Barometer.  —  The  barometer  is  an  instrument 
for  measuring  the  pressure   of  the   atmosphere.      It  is  a 
Torricellian  tube  furnished  with  a  convenient  case  (Figure 
102).     The  vessel  of  mercury  at  the  bottom  must  be  con- 
structed so  as  to  prevent  the  spilling  of  the  mercury  in 
transportation,  and  so  as  to  allow  the  atmosphere  to  act 
freely  upon  the  mercury. 

One  of  the  best  forms  of  the  cistern  for  holding  the  mer- 
cury is  shown  in  Figure  103.  The  upper  part  of  the  cistern  is 
a  cylinder  of  glass,  the  middle  part  is  a  cylinder  of  box-wood, 


io6 


NATURAL    PHILOSOPHY. 


and  the  bottom  of  the  cistern  is  of  leather,  and  may  be  raised 
Fig.  102.  °r  lowered  by  means  of  the  screw  p-;g  I03 
below.  The  top  of  the  cistern  is 
mainly  of  wood,  but  just  around 
the  tube  where  it  enters  the  cis- 
tern is  a  piece  of  leather,  fastened 
firmly  to  the  neck  of  the  tube  and 
to  the  collar  of  the  wooden  cup. 
This  leather  serves  the  double 
purpose  of  preventing  the  mercury 
from  escaping  when  the  barometer 
is  inverted,  and  of  allowing  the 
air  free  access  through  its  pores 
to  the  mercury  in  the  cistern. 
When  the  barometer  is  in  use, 
the  screw  at  the  bottom  of  the 
cistern  must  be  so  adjusted  that 
the  free  surface  of  the  mercury 
will  just  touch  the  ivory  point  seen 
at  the  right ;  when  the  barometer 
is  in  transportation,  the  screw  at 
the  bottom  is  turned  up  till  the 
mercury  presses  against  the  top 
of  the  cistern. 

148.  Use  of  the  Barometer  in  measuring  the 
Height  of  Mountains.  —  One  of  the  chief  uses 
of  the  barometer  is  to  measure  the  height  of 
mountains.  It  has  already  been  stated  that 
the  atmospheric  pressure  is  less  as  the  height 
above  the  earth  is  greater.  When  we  have 
found  at  what  rate  it  diminishes,  we  can 
readily  find  the  height  of  mountains  by  means 
of  the  barometer.  We  have  to  find  the  difference  between 
the  readings  of  the  barometer  at  the  level  of  the  sea  and 
at  the  top  of  the  mountain.  This  shows  how  much  the 
pressure  has  diminished,  and  from  this  we  can  find  the 
height  of  the  mountain. 


NATURAL   PHILOSOPHY. 


I07 


If  the  pressure  of  the  atmosphere  decreased  uniformly 
as  we  ascend,  it  would  be  very  easy  to  find  the  elevation  of  a 
place  by  means  of  a  barometer.  But,  owing  to  the  variations 
in  the  density  of  the  air  as  we  ascend,  the  pressure  changes 
according  to  a  complicated  law ;  and  this  complicates  the 
formula  for  finding  the  exact  elevation  of  a  place  from  the 
readings  of  the  barometer.  As  a  rough  rule,  it  may  be 
stated  that  the  barometer  falls  one  inch  for  every  900  feet 
of  ascent. 

149.  Suction- Pump.  —  The  suction-.pump  consists  of  a 
cylinder,  or  barrel,  at  the  top  of  a  pipe  A  (Figure  104), 
communicating  with  the  water  in  the  Fig.  104. 

reservoir.  A  piston  P  is  moved  up 
and  down  in  the  barrel  by  means  of 
the  handle  B.  There  is  a  valve  S  at 
the  top  of  the  tube  leading  into  the 
reservoir,  and  another  valve  O  in  the 
piston.  Both  valves  open  upward. 
The  pump  first  exhausts  the  air  from 
the  pipe.  As  the  air  is  exhausted, 
the  water  is  driven  up  through  the 
pipe  and  finally  into  the  pump-barrel 
by  the  pressure  of  the  air  on  the 
surface  of  the  water  in  the  cistern. 
Every  time  the  piston  is  pushed  down, 
the  valve  6"  closes,  and  keeps  the 
water  in  the  barrel  from  passing  back 
into  the  cistern ;  at  the  same  time  the 
valve  in  the  piston  opens,  and  allows 
the  water  in  the  barrel  below  it  to 
pass  above  it.  When  the  piston  is  Bp 
raised,  the  valve  O  closes,  and  keeps  ;:  ~~J\ 

the  water  above  it  from  passing  below 
it ;  at  the  same  time  the  valve  S  is 
forced  open  by  the  pressure  from  below,  and  the  water 


io8 


NATURAL    PHILOSOPHY. 


Fig.  105. 


rushes  up  through  it  to  fill  the  barrel  behind  the  piston. 
As  the  piston  is  raised,  the  water  above  the  piston  passes 
out  by  the  discharge-pipe  at  the  top  of  the  barrel.  With 
this  pump  the  water  is  raised  into  the  barrel  by  the  atmos- 
pheric pressure,  and  is  then  lifted  out  of  the  barrel  by 
the  piston.  Hence  with  the  suction- 
pump  water  can  be  raised  only  about 
30  feet  high. 

150.  Force-Pump.  —  The  simple 
force-pump  is  shown  in  Figure 
105.  The  piston  P  is  solid.  The 
discharge-pipe  D  communicates  with 
the  bottom  of  the  cylinder,  and  has 
a  valve  O  in  it  opening  upward. 
There  is  also  a  valve  6"  in  the  bot- 
tom of  the  barrel,  also  opening  up- 
ward. When  the  plunger  is  raised,  the 
valve  O  closes,  and  the  water  rushes 
into  the  cylinder  through  the  valve 
S  ;  when  the  plunger  is  pressed  down, 
the  valve  .S1  closes,  and  the  water  is 
forced  out  through  the  valve  O  into 
the  discharge-pipe.  The  only  limit 
to  the  height  to  which  water  may  be 
raised  by  means  of  this  pump  is  that, 
of  the  power  used  and  of  the  strength  of  the  pump. 

The  force-pump  and  the  suction-pump  may  be  combined, 
as  shown  in  Figures  106  and  107  ;  that  is  to  say,  the  cylin- 
der of  the  force-pump  may  be  at  the  top  of  a  pipe  about 
30  feet  above  the  surface  of  the  water  to  be  raised. 

151.  The  Air-Chamber.  —  The  air-chamber  is  a  device 
by  which  the  water  from  a  force-pump  may  be  made  to 
escape  in  a  continuous  and  forcible  stream.  It  consists 
of  an  air-tight  box  C  above  the  valve  O  in  the  discharge- 
pipe  (Figures  105  and  108).  The  pipe  D  passes  nearly 


NATURAL   PHILOSOPHY. 


I09 


to  the  bottom  of  the  chamber.  When  the  pump  is  working, 
the  water  is  forced  into  the  air-chamber  through  the  valve 
O.  As  soon  as  the  end  of  the  pipe  D  is  covered,  the  air 
in  the  upper  part  of  the  chamber  begins  to  be  compressed. 
The  compression  increases  the  elastic  force  of  the  air,  and 
causes  it  to  press  steadijy  and  forcibly  on  the  surface  of  the 


Fig.  106. 


Fig.  107. 


Fig.  108. 


water.  This  steady  pressure  forces  the  water  out  through 
the  pipe  Z?in  a  steady  stream.  If  D  ends  in  a  narrow  noz- 
zle, the  water  will  be  obliged  to  pass  through  it  very  rapidly 
to  escape  from  the  chamber  as  rapidly  as  it  is  pumped  into 
it.  In  this  way  a  stream  may  be  obtained  of  sufficient  force 
to  be  thrown  a  great  distance,  as  in  the  fire-engine. 

152.  The  Siphon.  —  The  siphon  is  used  for  transferring 
liquids  from  one  vessel  to  another.  It  consists  of  a  bent 
tube  C ' M B  (Figure  109),  with  arms  of  unequal  length. 
The  air  must  be  removed  from  the  tube  in  the  first  place, 
either  by  applying  the  mouth  to  the  end  B,  after  the  other 
arm  of  the  siphon  has  been  introduced  into  the  vessel  of 
water,  or  by  filling  the  siphon  with  water  before  it  is 
placed  in  the  vessel. 


NATURAL   PHILOSOPHY. 


The  water  will  flow  through  the  siphon  from   C  to  B 
until  the  vessel  is  emptied,  or  until  the  level  of  the  water 
Fig.  109.  falls  below  the  mouth  of  the 

arm  in  the  vessel.  The 
flow  of  the  liquid  through 
the%  siphon  seems  opposed 
to  the  well-known  fact  that 
water  will  not  run  up  hill. 
But  notwithstanding  this 
seeming  inconsistency,  it 
will  be  seen  that  the  water 
is  flowing  from  a  higher 
level  C  to  a.  lower  level  B. 
If  we  consider  a  layer  of 
water  in  the  siphon  at  M, 
we  see  that  the  force  which 
acts  upon  it  from  left  to  right  is  equal  to  the  pressure  of 
the  atmosphere  minus  the  pressure  of  the  water  in  the 
tube  from  M  to  C,  whose  depth  is  D  C ;  and  the  pressure 
which  acts  upon  it  from  right  to  left  is  equal  to  the  pres- 
sure of  the  atmosphere  minus  the  pressure  of  the  water  in 
the  tube  from  M  to  B,  whose  depth  is  A  B.  Since  A  B  is 
greater  than  D  C,  the  pressure  at  M  towards  the  right  will 
be  greater  than  that  towards  the  left.  Consequently,  the 
water  at  M  moves  on  towards  B,  and  as  it  moves  away 
more  water  is  driven  up  into  the  arm  CM  to  take  its  place 
by  the  pressure  of  the  atmosphere  on  the  surface  of  the 
water  in  the  vessel.  No  liquid  will  flow  through  a  siphon 
unless  the  atmospheric  pressure  is  sufficient  to  raise  it  to 
the  bend  of  the  tube. 

153.  Tantalus's  Clip.  —  This  is  a  glass  cup,  with  a  si- 
phon tube  passing  through  the  bottom,  as  shown  in  Figure 
no.  If  water  is  poured  into  the  cup,  it  will  rise  both 
inside  and  outside  the  siphon  until  it  has  reached  the 
top  of  the  tube,  when  it  will  begin  to  flow  'out.  If  the 


NATURAL    PHILOSOPHY. 


water  runs  into  the  cup  less  rapidly  than  the  siphon  carries 
it  out,  it  will  sink  in  the  cup  until  the  shorter  arm  no 
longer  dips  into  the  liquid,  and  Fig.  no. 

the  flow  from  the  siphon  ceases. 
The  cup  will  then  fill,  as  before ; 
and  so  on. 

In  many  places  there  are  springs 
which  flow  at  intervals,  like  the 
siphon  in  this  experiment,  and 
whose  action  may  be  explained  in 
the  same  way.  A  cavity  under 
ground  (Figure  in)  may  be  grad- 
ually filled  with  water  by  springs,  and  then  emptied  through 
an  opening  which  forms  a  natural  siphon.  In  some  cases 
of  this  kind  the  flow  stops  and  begins  again  several  times 
in  an  hour. 

Fig.  in. 


1 54.  Efflux  of  Liquids.  —  If  an  opening  is  made  in  the  side 
of  a  vessel  containing  water,  the  liquid  escapes  from  the  opening 
with  a  velocity  which  increases  with  the  depth  of  the  orifice  be- 
low the  surface  of  the  water  in  the  vessel.  The  height  of  the 
water  above  the  orifice  is  called  the  head  of  the  water.  Torri- 


112  NATURAL   PHILOSOPHY. 

celli  arrived,  by  experiment,  at  the  conclusion  that  the  velocity  of 
efflux  is  equal  to  that  which  a  body  would  acquire  by  falling  freely 
from  the  surface  of  the  water  to  the  centre  of  the  orifice.  If  the 
height  of  the  surface  of  the  water  above  the  centre  of  the  orifice 
is  represented  by  /i,  the  velocity  of  efflux  would  be  given  by  the 
formula 

V '  =  «J~^g~h. 

It  is  assumed  that  the  sides  of  the  vessel  are  thin,  and  that  the 
diameter  of  the  orifice  is  very  small  compared  with  that  of  the 
vessel.  The  jet  issuing  from  the  orifice  is  parabolic.  By  measur- 
ing its  range,  we  can  calculate  the  velocity  of  efflux. 

Fig.   112. 


An  apparatus  for  measuring  the  range  of  the  jet  is  shown  in 
Figure  112.  It  consists  of  a  cylinder,  in  which  are  a  number  of 
equidistant  orifices  in  the  same  vertical  line.  A  faucet  above 
supplies  the  cylinder  with  water,  and  with  the  help  of  an 
overflow-pipe  keeps  the  water  at  a  constant  level,  which  is  as 
much  above  the  highest  orifice  as  each  orifice  is  above  that  next 
below  it.  The  liquid  which  escapes  is  received  in  a  trough,  the 
edge  of  which  is  graduated.  A  travelling-piece,  carrying  a  disc 


NATURAL    PHILOSOPHY.  113 

with  a  circular  aperture  in  its  centre,  slides  along  the  trough. 
The  travelling-piece  is  placed  so  that  the  jet  from  any  orifice 
passes  through  the  centre  of  the  aperture  in  the  disc.  The 
range  of  the  jet  is  then  indicated  on  the  edge  of  the  trough. 

It  is  found,  by  experiment,  that  the  quantity  of  water  discharged 
from  a  circular  orifice  is  less  than  would  be  obtained  by  multiply- 
ing the  size  of  the  orifice  by  the  velocity  of  discharge.  This 
is  because  the  particles  of  liquid  at  the  margin  of  the  orifice  have 
a  converging  motion,  in  consequence  of  which  the  jet  contracts 
rapidly  for  a  short  distance  from  the  orifice  (Figure  113).  The 
portion  of  the  jet  at  the  end  of  this  contraction  is  Fig  ,I3_ 
called  the  vena  contracta,  or  contracted  vein.  Its 
section  is  about  .6  that  of  the  orifice.  If  the  quan- 
tity of  discharge  is  calculated  by  multiplying  the 
section  of  the  vena  contracta  by  the  velocity  of 
efflux,  the  result  agrees  with  experiment. 

If  the  liquid  is  discharged  through  a  cylindrical 
tube  a  few  inches  long,  of  the  same  section  as  the 
orifice,  it  will  be  found  by  measurement  that  the 
velocity  has  decreased  somewhat,  but  the  amount  of  discharge 
obtained  by  calculation  will  agree  with  that  ascertained  by  ex- 
periment. The  adhesion  of  the  water  to  the  sides  of  the  tube 
prevents  the  contraction  of  the  vein,  and  also  diminishes  the 
velocity  of  the  jet  by  friction. 

When  the  liquid  flows  through  a  long  tube,  the  velocity  is  con- 
siderably reduced  by  the  friction  of  the  molecules  against  each 
other,  and  against  the  sides  of  the  tube.  The  velocity  is  also 
least  at  the  sides  of  the  tube,  and  greatest  at  the  centre. 

155.  Water-  Wheels.  —  One  of  the  most  important  sources 
of  mechanical  power  is  that  of  falling  water.  The  falling 
or  running  water  is  made  to  turn  a  wheel  called  a  water- 
wheel ;  and  this  wheel,  by  means  of  bands  or  gearing,  is 
made  to  work  almost  any  kind  of  machinery. 

Water-wheels  are"  of  various  forms.  Some  turn  on  an 
upright  axis,  and  others  on  a  horizontal  axis.  The  latter 
are  called  vertical  water-wheels,  and  the  former  horizontal 
water-wheels. 


n4 


NATURAL    PHILOSOPHY. 


One  of  the  most  common  of  vertical  water-wheels  is  rep- 
resented in  Figure  114.  It  consists  of  a  series  of  boxes, 

or    buckets,  arranged     on 
the  outside  of  a  wheel  or 
cylinder.      Water    is    al- 
lowed to  flow  into  these 
buckets  on  one  side  of  the 
wheel,   and   by  its  weight 
causes  the  wheel  to  turn. 
The  buckets  are  so  con- 
structed   that    they   hold 
water  as  long  as  possible 
while  they  are  going  down, 
but  allow  it  all  to  run  out 
before  they  begin  to  rise  on  the  other  side. 
A  wheel  like  this  is  called  a  breast-wheel. 
The  overshot  wheel  is  similar  to  the  breast-wheel  in  all 
respects,  except  that  the  water  is  led  over  the  top  of  the 
wheel,  and  poured  into  the  buckets  on  the  other  side. 

The  undershot  wheel  has  boards  projecting  from  its  cir- 
cumference, like  the  paddle-wheel  of  a  steamboat.  The 
water  runs  under  the  wheel,  and  turns  it  by  force  of  the  cur- 
rent pressing  against  the  boards. 

156.  The  Hydraulic  Tourniquet.  —  If  a  vessel  E  (Figure 
115),  having  a  spout  and  faucet  on  one  side,  is  filled  with 
water  and  floated  in  a  dish  on  water 
so  as  to  move  easily,  on  opening  the 
faucet  so  as  to  allow  the  water  to 
escape,  the  vessel  will  begin  to  move 
backward.  This  is  due  to  the  reac- 
tion of  the  water  against  the  back 
of  the  vessel.  While  the  faucet  was 
closed,  the  pressure  of  the  water 
against  the  front  of  the  vessel  at  the 
orifice  balanced  the  pressure  of  the 


NATURAL    PHILOSOPHY. 


water  against  the  back  of  the  vessel  at  the  same  point. 
But  when  the  faucet  is  open,  there  is  no  pressure  against 
the  front  of  the  vessel  to  balance  the  reaction  of  the  water 
against  the  back  of  the  vessel ;  hence  the  backward  motion 
of  the  vessel  while  the  latter  is  escaping. 

The  hydraulic  tourniquet  (Figure  116)  consists  of  a  ves- 
sel capable  of  rotating  on  a  vertical  axis.     Two  tubes  pro- 
ject from  the  bottom  Fig  n6. 
of 'the  vessel  in  oppo- 
site directions.     The 
ends  of   these   tubes 
are     open,    and    are 
bent  round  in  oppo- 
site   directions.      As 
the     water     escapes 
from  these  tubes,  the 
vessel    is     put     into 
rapid  rotation  by  the     /• 
reaction  of  the  water    | 
against   the   parts  of    ' 
the  tubes  opposite  the 
openings. 

157.  Turbine  Wheel. — One  form  of  the  turbine  wheel  is 
shown  in  Figure  117.  This  wheel  turns  in  a  horizontal 
plane.  The  buckets  are  placed  in  the  outer  part  of  the 
wheel,  which  is  free  to  turn  on  a  vertical  axis.  The  curved 
partitions,  or  guides,  within  the  wheel  are  stationary.  These 
partitions  are  placed  at  the  bottom  of  a  long  cylinder,  into 
which  the  water  is  admitted  by  the  pipe.  The  partitions 
are  curved,  so  as  to  direct  the  water  against  the  buckets 
at  the  most  advantageous  angle.  The  water  is  discharged 
at  the  rim  of  the  wheel.  Figure  118  is  a  section  of  a 
turbine  wheel.  The  buckets  are  represented  in  the  outer 
portion,  and  the  guides  in  the  inner  circle. 

There  are  many  kinds  of  turbines,  and  their  effective 


n6 


NATURAL   PHILOSOPHY. 

Fig.  1 1 8. 


power  is  from  75  to  88  per  cent 
of  that  in  the  acting  body  of 
water.  In  the  best  form  of  over- 
shot and  breast  wheels,  it  is  from 
65  to  75  per  cent,  and  in  under- 
shot wheels  from  25  to  33  per  cent. 

E.   SOLIDS. 

158.  Tendency  of  Solids  to  assume  a  Crystalline  Struc- 
ture.—  Solids,  as  a  rule,  tend  to  assume  a  crystalline 
structure.  This  tendency  is  best  shown  by  allowing  a 
substance  to  pass  gradually  from  a  liquid  to  a  solid  state. 
Place  a  rather  dilute  solution  of  acetate  of  lead  in  a  tank 
with  parallel  sides  of  glass  (such  as  are  often  used  for  pro- 
jection), and  fix  two  platinum  wires  in  the  solution,  about 
an  inch  apart.  Place  the  tank  before  the  condenser  of  a 
magic  lantern,  and  focus  the  wires  on  the  screen.  Con- 
nect the  wires  with  the  poles  of  a  small  voltaic  battery. 
The  lead  will  separate  from  the  solution,  and  collect  as 
a  solid  upon  the  wire  connected  with  the  negative  pole 
of  the  battery.  Beautiful  fern-like  forms  will  be  seen  to 
grow  up  on  the  screen.  These  forms  are  the  crystals  of 
lead.  As  the  substance  passes  slowly  from  the  liquid  to 


NATURAL   PHILOSOPHY.  117 

the  solid  state,  the  molecules  are  free  to  arrange  them- 
selves according  to  their  tendencies. 

If  alum  is  added  to  hot  water  as  long  as  it  will  dis- 
solve, and  then  the  water  is  allowed  to  cool  slowly,  a  part 
of  the  alum  will  be  deposited  on  the  bottom  of  the  dish, — 
not  in  a  confused  mass,  but  in  beautiful  crystals.  If  salt- 
petre, nitrate  of  baryta,  or  corrosive  sublimate  is  treated 
in  the  same  way,  beautiful  crystals  will  be  formed,  but  in 
each  case  the  crystals  will  have  a  different  shape. 

Melt  some  sulphur  in  a  crucible,  and  allow  it  to  cool 
slowly  till  a  crust  forms  on  the  sur-  Fig.  119. 

face  ;  then  carefully  break  the  crust 
and  pour  off  the  remaining  liquid, 
and  the  crucible  will  be  found  lined 
with  delicate  needle-shaped  crystals 
(Figure  119). 

Large  crystals  of  many  solids  can 
be  obtained  by  dissolving  as  much  of 
the  solid  as  is  possible  in  cold  water, 
and  then  setting  it  away  in  a  shallow  dish  where  it  will  be 
free  from  dust  and  disturbance,  and  allowing  the  water  to 
evaporate  very  slowly.  The  more  gradual  the  formation, 
the  larger  are  the  crystals.  The  larger  crystals  seen  in 
cabinets  of  minerals  were  probably  centuries  in  forming. 
The  water  in  which  the  solid  was  dissolved  found  its  way 
into  a  cavity  of  a  rock,  and  there  slowly  evaporated. 

The  tendency  of  the  cohesive  force  to  form  the  molecules 
into  crystals  is  strikingly  shown  in  cannon  which  have  been 
many  times  fired,  and  in  shafts  of  machinery  and  axles  of 
car-wheels  which  are  continually  jarred.  Such  bodies  often 
become  brittle,  and  on  breaking  show  the  smooth  faces 
of  the  crystals  which  have  been  formed.  The  continued 
jarring  gives  the  molecules' a  slight  freedom  of  motion,  and 
crystals  are  slowly  built  up. 

Many  solids  are  crystalline  in  structure  which  do  not 


n8  NATURAL  PHILOSOPHY. 

appear  to  be  so.  Thus,  a  piece  of  ice  is  a  mass  of  the 
most  perfect  crystals,  but  they  are  so  closely  packed  to- 
gether that  we  cannot  readily  distinguish  them. 

159.  Properties  of  Solids.  —  A  body  is  said  to  be  tena- 
cious when  it  is  difficult  to  pull  it  in  two.  All  solids  are 
more  or  less  tenacious,  but  they  differ  greatly  in  the  degree 
of  their  tenacity.  A  body  is  said  to  be  hard  when  it  is 
difficult  to  scratch  or  indent  it,  that  is  to  say,  when  it 
is  difficult  to  displace  its  molecules.  All  solids  are  elastic 
within  certain  limits,  and  this  elasticity  may  be  developed 
by  stretching,  by  bending,  by  twisting,  and  by  compres- 
sion, that  is,  by  any  kind  of  strain  whate.ver.  Different 
solids,  however,  differ  greatly  in  the  limit  of  their  elasticity. 
When  the  strain  is  carried  beyond  the  limit  of  elasticity, 
the  body  must  either  break  or  take  up  permanently  a  new 
form.  A  body  which  is  apt  to  break  when  strained  beyond 
the  limit  of  elasticity  is  said  to  be  brittle.  A  brittle  sub- 
stance is  not  always  easily  broken.  Such  a  body  will  not 
break  unless  strained  beyond  the  limit  of  its  elasticity,  and 
that  is  often  a  difficult  thing  to  do.  It  is  not  easy  to  break 
a  glass  rod  an  inch  in  diameter,  yet  glass  is  the  most  brit- 
tle substance  known.  Substances  which  can  readily  take 
permanently  new  forms  are  said  to  be  malleable  or  ductile. 
A  malleable  substance  is  one  that  can  be  hammered  or 
rolled  into  sheets,  and  a  ductile  substance  one  that  can 
be  drawn  into  wire.  All  malleable  substances  are  to  some 
extent  ductile,  but  the  most  malleable  are  not  the  most 
ductile. 

Gold  is  one  of  the  most  malleable  of  the  metals.  In  the 
manufacture  of  gold-leaf,  it  is  hammered  out  into  sheets  so 
thin  that  it  takes  from  300,000  to  350,000  of  them  to  make 
the  thickness  of  a  single  inch. 

The  gold  is  first  rolled  out  into  sheets  by  passing  it 
many  times  between  steel  rollers  in  what  is  called  a  rolling- 
machine.  The  rollers  are  so  arranged  that  they  can  be 


NATURAL    PHILOSOPHY.  119 

brought  nearer  to  each  other,  pressing  the  gold  into  a 
thinner  and  thinner  sheet  every  time  it  is  passed  between 
them.  After  it  has  thus  been  rolled  out  to  the  thick- 
ness of  writing-paper,  it  is  cut  up  into  pieces  about  an 
inch  square.  These  are  piled  into  a  stack  with  alternate 
pieces  of  tough  paper,  and  beaten  with  wooden  mallets. 
They  are  again  cut  up  into  small  pieces,  and  arranged  in  a 
stack  with  alternate  squares  of  gold-beater's  skin,  and 
again  beaten  with  mallets.  This  last  process  is  usually 
repeated  three  times. 


II. 

SOUND. 
A.   ORIGIN. 

160.  Sound  originates  in  Molar  Vibrations.  —  Fix  a 
point  on  a  stand  so  as  to  be  nearly  in  contact  with  a  glass 
bell  (Figure  120),  and  also  hang  a  pith  ball  in  contact 


with  the  bell  on  the  opposite  side.  If  we  draw  a  rosined 
bow  across  the  edge  of  the  bell,  this  will  be  made  to  emit 
a  musical  sound,  and  will  also  be  heard  to  tap  against 
the  point,  showing  that  it  is  in  vibration.  The  pith  ball 
will  also  be  kept  swinging  as  long  as  the  sound  continues. 
On  touching  the  bell  lightly,  we  feel  that  it  is  vibrating. 


NATURAL    PHILOSOPHY. 


By  grasping  it  firmly,  we  stop  both  the  vibration  and  the 
sound. 

Strike  one  prong  of  a  tuning-fork,  and  hold  it  to  the  ear ; 
it  is  found  to  be  emitting  sound.  Fill  a  glass  brimful  of 
water,  and  hold  the  edge  of  the  prongs  in  contact  with  the 
water  ;  a  shower  of  spray  will  fly  off  on  each  side,  showing 
that  the  prong  is  in  vibration. 

When  a  string  or  wire  is  emitting  a  sound,  it  may  often 
Fig.  121.      be  seen  to  be  vibrating.     It  as-         Fig.  122. 

sumes  the  form  of  an  elongated 

spindle  (Figure  121). 

If  the  front  of  an  organ  pipe 

is   made  of  glass,  and  a  little 

stretched    membrane     covered 

with   sand   is   lowered    into   it 

(Figure  122),  when  the  pipe  is 

emitting  a  sound,  the  sand  will 

be  seen  to  be  agitated,  showing 

that  the  air  within  the  pipe  is  in 

a  state  of  vibration. 

By  similar  experiments  it  has 
been  ascertained  that  every  body  which  is 
emitting  sound  is  in  a  state  of  molar  vibra- 
tion. When  the  vibration  stops,  the  sound 
ceases.  The  more  intense  the  vibration,  the 
louder  the  sound.  Sound,  therefore,  origi- 
nates in  molar  vibration  of  ordinary  matter, 
solid,  liquid,  or  gaseous. 

161.  Fundamental  and  Harmonic  }*ib ra- 
tions. —  Strew  sand  upon  a  horizontal  plate 
of  brass,  and  then,  holding  it  with  the 
thumb  and  finger  (Figure  123),  draw  a 
bow  across  the  edge  of  the  plate  so  as  to  throw  it  into 
vibration.  The  sand  will  be  tossed  up  and  down  at  first, 
but  will  quickly  come  to  rest  in  definite  lines,  called  nodal 


122 


NATURAL  PHILOSOPHY. 


lines.     These  are  lines  of  rest  which  separate  the  vibrat- 
ing segments  of  the  plate.     By  touching  the  plates  at  dif- 

Fig.  123. 


ferent  points  with  the  thumb  and  fingers,  a  great  variety 
of  figures  may  be  produced  with  the  sand,  showing  that  it 
is  possible  for  the  plate  to  break  up  into  vibrating  segments 
in  a  great  many  different  ways.  A  series  of  these  nodal 
figures  is  shown  in  Figure  125. 

Strings  and  columns  of  air  may  be  also  made  to  vibrate 
in  segments.     Figure  124  shows  a  string  vibrating  as  a 

Fig.  124. 


whole,  in  two  segments,  in  three  segments,  and  in  four 
segments. 

The  vibration  of  a  body  as  a  whole  is  called  its  funda- 


NATURAL    PHILOSOPHY. 
Fig.  125. 


123 


124 


NATURAL   PHILOSOPHY. 


mental  vibration ;  and  the  vibration  of  its  segments,  its 
harmonic  vibration.  The  harmonic  vibrations  are  more 
rapid  than  the  fundamental  vibrations.  In  a  complete 
series  of  harmonic  vibrations,  the  rate  of  vibration  in  the 
first  harmonic  is  twice  the  fundamental  rate;  in  the  second 
harmonic,  three  times  the  fundamental  rate  ;  in  the  third 
harmonic,  four  times  the  fundamental  rate  ;  and  so  on. 
Usually  some  of  the  members  of  the  series  of  harmonic 
vibrations  are  wanting  in  the  case  of  vibrating  bodies. 

It  is  not  only  possible  to  produce  harmonic  vibrations  in 
a  body,  but  it  is  almost  impossible  not  to  produce  them 
when  a  body  is  thrown  into  vibration.  Whenever  the  funda- 
mental vibration  of  a  body  is  started,  some  of  the  harmonic 
vibrations  are  almost  certain  to  be  started  with  it.  Hence 
Fig.  126.  it  follows  that  the  molar  vibra- 

tions of  bodies  which  originate 
sound  are  more  or  less  com- 
plicated. 

B.   PROPAGATION  OF  SOUND. 

162.  Sound  is  not  propagated 
in  a  Vacuum.  —  In  Figure  126 
the  bell  B  is  suspended  by 
silk  threads  under  the  re- 
ceiver of  the  air-pump.  The 
bell  is  struck  by  means  of 
clock-work,  which  can  be  set 
in  motion  by  the  sliding-rod  r. 
If  the  bell  is  struck  before 
exhausting  the  air,  it  can  be 
distinctly  heard ;  but  as  the 
air  is  exhausted,  the  sound 
becomes  fainter  and  fainter, 
until  at  last  it  can  hardly  be 


NATURAL   PHILOSOPHY.  125 

perceived,  even  with  the  ear  close  to  the  receiver.     Sound, 
then,  cannot  pass  through  a  vacuum. 

The  slight  sound  which  is  heard  is  transmitted  by  the 
little  air  left  in  the  receiver,  and  by  the  cords  which  hold 
up  the  bell. 

1 63.  Sound  is  propagated  in  Gases,  Liquids,  and  Solids.  — 
If  hydrogen  or  any  other  gas  is  now  allowed  to  pass  into 
the  receiver,  the  sound  of  the  bell  is  heard  again.     If  a 
bell  is  put  under  water  and  struck,  it  can  be  heard.     If 
a  person  puts  his  ear  close  to  the  rail  of  an  iron  fence,  and 
the  rail  is  struck  at  a  considerable  distance,  he  hears  the 
blow  twice.     The  first  sound  comes  through  the  rail ;  the 
second,  which  soon  follows,  comes  through  the  air.     These 
experiments  show  that  sound  passes  through  gases,  liquids, 
and  solids.     Sounds  are  propagated  chiefly  by  the  air. 

164.  Sound  is  propagated  by  Waves.  —  When  any  vibrat- 
ing body,  as  the  prong  of  a  tuning-fork,  is  moving  forward, 
it  crowds  together  the  molecules  of  the  air  in  front  of  it, 
and  so  produces  a  strain  of  compression  in  the  air.     As 
the  body  moves  back  again  to  its  original  position  and 
beyond  it  on  the  other  side,  it  willows  the  molecules  of  the 
air  behind  it  to  separate  somewhat,  and  so  produces  a 
strain  of  rarefaction  in  the  air.     Each  of  these  strains  is 
propagated  through  the  air  from  molecule  to  molecule  in 
precisely  the  same  way  that  the  strain  of  compression  was 
propagated  from  ball  to  ball  in  Figure  8.     The  molecules 
of  air  in  front  of  the  vibrating  body  simply  vibrate  to  and 
fro  with  the  sounding  body.     This  vibrating  motion  is  also 
propagated  from  molecule  to   molecule  through  the  air; 
but  while  the  strains  of  compression  and  rarefaction  are 
continually  moving  forward,  each   molecule  of  air  moves 
forward  a  short  distance  and  then  returns. 

The  strains  of  compression  and  rarefaction  constitute 
what  is  called  a  sound-wave,  and  each  strain  is  called  a 
phase  of  the  wave.  If  the  body  continues  in  vibration, 


126 


NATURAL   PHILOSOPHY. 


the  phases  of  the  waves  will  follow  each  other  in  regular 
succession. 

The  distance  occupied  by  the  two  strains  or  phases  is 
called  the  length  of  the  wave.  As  the  strain  of  compres- 
sion is  formed  while  the  vibrating  surface  is  moving  for- 
ward, and  the  strain  of  rarefaction  while  the  surface  is 
moving  backward,  the  length  of  each  of  these  phases  will 
be  the  distance  the  strain  propagates  itself  while  the 
sounding  body  performs  half  a  vibration,  and  the  length  of 
the  sound-wave  will  be  the  distance  the  strain  can  propa- 
gate itself  while  the  sounding  body  is  making  a  complete 
vibration.  Hence,  the  faster  the  sounding  body  vibrates 
the  shorter  the  sound-waves,  and  the  slower  it  vibrates  the 
longer  the  waves. 


Since  the  sound-wave  travels  at  the  same  rate  in  all 
directions  in  an  open  space,  the  outer  surface  of  an  ad- 
vancing sound-wave  is  spherical.  Figure  127  is  a  section 


NATURAL   PHILOSOPHY.  127 

of  a  series  of  sound-waves  advancing  from  a  point  at  the 
centre  of  the  section. 

165.  The  Intensity  of  Sound.  —  The  intensity  of  sound 
at  any  point  depends  upon  the  energy  of  the  vibration  of 
the  molecules  at  that  point. 

As  the  sound-waves  spread  in  all  directions  from  the 
sounding  body,  a  greater  and  greater  number  of  particles  of 
air  must  be  set  in  motion,  and  the  motion  of  each  must  be 
more  feeble;  and  since  the  surfaces  of  spheres  increase  as 
the  squares  of  their  radii,  the  number  of  particles  to  be  set 
in  motion  increases  as  the  square  of  the  distance  from  the 
sounding  body.  Sound,  then,  diminishes  in  intensity  as  the 
square  of  the  distance  from  the  sounding  body  increases. 

If  the  sound-waves  are  prevented  from  spreading  in  all 
directions,  the  particles  of  air  lose  little  of  their  motion, 
and  the  sound  little  of  its  intensity.  Thus,  Biot  found  that 
through  one  of  the  water-pipes  of  Paris  words  spoken  in  a 
very  low  tone  could  be  heard  at  the  distance  of  about  three 
quarters  of  a  mile.  The  sides  of  the  pipe  kept  the  sound- 
waves from  spreading.  In  the  same  way  conversation  can 
be  carried  on  between  distant  parts  of  a  large  building  by 
means  of  small  tubes,  called  speaking-tubes. 

1 66.  The  Velocity  of  Sound.  —  The  velocity  of  sound  in  air 
has  been  several  times  determined  by  experiment.    In  1822 
the  French  Board  of  Longitude  chose  two  heights  near  Paris, 
and  from  the  top  of  each  fired  a  cannon  at  intervals  of  ten 
minutes  during  the  night.     The  time  between  seeing  the 
flash  and  hearing  the  report  was  carefully  noted  at  both 
stations,  and  the  average  of  the  results  showed  that  sound 
travels  through  the  air  at  the  rate  of  1090  feet  a  second. 
In  such  experiments  the  time  taken  by  the  light  to  pass 
between  the  stations  is  too  small  to  be  perceived. 

The  velocity  of  sound  in  air  depends  somewhat  upon  the 
state  of  the  atmosphere.  Sound-waves  travel  faster  with 
the  wind  than  against  it,  and  the  higher  the  temperature  of 


128  NATURAL    PHILOSOPHY. 

the  air,  the  greater  the  velocity  of  sound  in  it.    The  velocity 
given  above  is  for  the  temperature  of  32°. 

The  velocity  of  sound  in  water  is  about  4700  feet  a 
second,  and  its  velocity  in  solids  is  still  greater. 

167.  The  Reflection  of  Sound.  —  When  sound-waves  meet 
the  surface  of  a  new  medium,  they  are,  in  part,  thrown 
back,  or  reflected.     In  this  reflection,  as  in  all  cases  of  re- 
flected motion,  the  angles  of  incidence  and  reflection  are 
equal  to  each  other. 

Echoes  are  produced  by  the  reflection  of  sound.  In  order  to 
get  an  echo,  we  must  have  a  reflecting  surface  far  enough  away 
to  give  an  appreciable  interval  between  the  direct  and  reflected 
sounds.  When  the  surface  is  less  than  100  feet  distant,  the 
reflected  sound  blends  with  the  direct  sound. 

The  reflecting  surface  has  often  such  a  shape  as  to  cause  the 
different  portions  of  the  reflected  wave  to  converge  to  a  point, 
and  so  to  intensify  the  reflected  sound. 

Multiple  echoes  may  be  produced  by  successive  reflections 
from  surfaces  at  different  distances  on  the  same  side,  or  by 
alternate  reflections  from  two  surfaces  on  opposite  sides.  In 
some  localities  a  pistol-shot  is  repeated  thirty  or  forty  times. 

Sound-waves  are  partially  reflected  on  meeting  a  layer  of  air 
of  a  different  density  from  that  which  they  are  traversing.  Such 
layers  of  air  often  exist  side  by  side  in  the  atmosphere.  This 
is  one  reason  why  the  same  sound  will  sometimes  penetrate  the 
atmosphere  to  a  much  greater  distance  than  at  others.  The 
atmosphere  is  at  such  times  free  from  these  reflecting  strata, 
which  tend  to  stop  the  sound. 

168.  The  Refraction  of  Sound.  —  When  a  portion  of  a  sound- 
wave enters  obliquely  a  new  medium  in  which  it  travels  at  a 
different  rate  from  that  in  the  old,  it  experiences  a  change  of 
front  which  alters  the  direction  of    the  sound.     This  change 
of  direction  of  sound  on  entering  a  new  medium  is  called   re- 
fraction. 

Let  a  b  (Figure  128)  represent  a  portion  of  a  sound-wave 
moving  in  the  direction  of  the  arrow,  and  a  c  be  the  surface  of 
a  medium  O,  of  different  density  from  M,  in  which  the  wave  has 
been  moving.  If  the  elasticity  of  O  is  such  that  the-  wave  will 


NATURAL   PHILOSOPHY. 


I29 


move  faster  in  it  than  in  Af,  the  portion  a  of  the  wave  which 
enters  O  first  will  move  on  faster  than  the  portion  b,  while  the 
latter  is  moving  in  M.  When  a  b  is  wholly  within  O,  the  second 
arrow  shows  the  direction  in  which  it  will  be  moving ;  and  it 
will  continue  to  move  in  this  direction  so  long  as  it  is  wholly  in 
this  medium.  In  this  case  the  sound-wave  is  bent  away  from  a 
perpendicular  P  Q  drawn  to  the  surface  of  the  medium  O. 

If  the  elasticity  of  O  is  such  that  the  sound-wave  moves 
slower  in  it  than  in  M,  the  portion  a  of  the  wave  (Figure  129), 
when  it  has  entered  O,  moves  slower  than  6,  while  the  latter  is 
in  M.  In  this  case  it  will  be  seen  that  the  direction  of  the  wave 
will  be  bent  towards  the  perpendicular  P  Q. 

Fig.  «* 


It  is  evident  that  if  a  b  had  not  met  the  medium  O  obliquely, 
both  ends  of  it  would  have  entered  O  at  the  same  time,  and  its 
direction  would  not  have  been  changed. 

We  see,  then,  that  when  a  sound-wave  passes  obliquely  into 
a  medium  of  different  density,  it  is  refracted,  and  that,  if  it 
travels  more  rapidly  in  the  new  medium,  it  will  be  bent  away 
from  a  perpendicular  drawn  to  the  surface  of  that  medium  ; 
while,  if  it  travels  less  rapidly  in  the  new  medium,  it  will  be 
bent  towards  a  perpendicular  drawn  to  the  surface  of  that 
medium. 

By  refraction  in  passing  from  one  layer  of  air  to  another, 
sounds  may  be  made  to  pass  over  the  head  of  an  observer  with- 
out being  heard  by  him  at  all.  This  is  probably  one  reason 
why  sounds  which  are  ordinarily  audible  in  certain  localities  are 


130  NATURAL   PHILOSOPHY. 

at  other  times  not  heard  at  all.  At  other  times,  especially  in 
hilly  regions,  sounds  which  are  ordinarily  inaudible,  because 
they  pass  overhead,  may  have  their  direction  so  changed  by 
refraction  or  reflection  as  to  reach  the  ear. 

169.    Speaking    and    Ear     Trumpets.  —  The    speaking- 
trumpet  (Figure  130)  consists  of  a  long  tube  (sometimes 

Fig.  130. 


six  feet  long),  slightly  tapering  towards  the  speaker,  fur- 
nished at  this  end  with  a  hollow  mouth-piece,  which  nearly 
fits  the  lips,  and  at  the  other  with  a  funnel-shaped  enlarge- 
ment, called  the  bell,  opening  out  to  a  width  of  about  a 
foot.  It  is  much  used  at  sea,  and  is  found  very  effectual 
in  making  the  voice  heard  at  a  distance.  The  explanation 
usually  given  of  its  action  is,  that  the  slightly  conical  form 
of  the  long  tube  produces  a  series  of  reflections  in  direc- 
tions more  and  more  nearly  parallel  to  the  axis ;  but  this 
explanation  fails  to  account  for  the  utility  of  the  bell,  which 
experience  has  shown  to  be  considerable. 

The  ear-trumpet  is  used  by  persons  who  are  hard  of  hear- 
ing. It  is  essentially  an  inverted  speaking-trumpet,  and 
consists  of  a  conical  metallic  tube,  one  of  whose  extremi- 
ties, terminating  in  a  bell,  receives  the  sound,  while  the 
other  end  is  introduced  into  the  ear.  This  instrument  is 
the  reverse  of  the  speaking-trumpet.  The  bell  serves  as 
a  mouth-piece ;  that  is,  it  receives  the  sound  coming  from 
the  mouth  of  the  person  who  speaks.  These  sounds  are 
transmitted  by  a  series  of  reflections  to  the  interior  of  the 
trumpet,  so  that  the  waves,  which  would  become  greatly 
developed,  are  concentrated  on  the  auditory  apparatus,  and 
produce  a  far  greater  effect  than  divergent  waves  would 
have  done. 


NATURAL   PHILOSOPHY.  131 

170.  The  Form  of  Sound-Waves.  — The  phases  of  compres- 
sion and  rarefaction  in  a  sound-wave  correspond  to  the  elevation 
and  depression  of  a  water-wave.  In  the  case  of  water-waves 
the  molecules  are  vibrating  up  and  down  across  the  direction  in 
which  the  wave  is  moving,  that  is  to  say,  transversely.  In  the 
case  of  sound-waves  the  molecules  are  vibrating  to  and  fro 
in  the  direction  in  which  the  wave  is  moving,  or  longitudinally. 
In  water-waves  the  molecules  vibrate  up  and  down  in  paths 
which  are  nearly  circles. 

Imagine  the  waves  of  water  pressed  flat  without  any  lateral 
spreading  of  the  molecules.  Where  the  waves  were  highest, 
the  molecules  of  the  flattened  waves  would  be  crowded  closest 
together,  and  where  the  waves  were  lowest  the  molecules  would 
be  farthest  apart.  The  elevation  and  depression  of  the  waves 
would  be  converted  into  phases  of  compression  and  rarefac- 
tion. Moreover,  the  vertical  circles  in  which  the  molecules  of 
water  are  moving  would  be  flattened  into  straight  lines,  and  the 
molecules  would  vibrate  longitudinally.  By  such  flattening  a 

Fig.  131. 


water-wave  would  be  converted  into  a  sound-wave,  and  the  origi- 
nal form  of  the  water-wave  would  be  represented  by  certain 
states  of  compression  in  the  different  phases  of  the  new  wave. 

By  a  reverse  transformation,  the  state  of  compression  and 
rarefaction  in  a  sound-wave  may  be  represented  by  a  form  simi- 
lar to  that  of  the  water-wave. 

If  we  represent  the  state  of  compression  or  rarefaction  of  a 
sound-wave  by  a  curve,  the  height  of  which  at  each  point  repre- 
sents the  degree  of  compression  or  rarefaction  at  that  point,  the 
curve  will  be  highest  where  the  condensation  is  greatest,  and 
lowest  where  the  rarefaction  is  greatest.  Such  a  curve  would 
have  a  form  similar  to  that  of  a  water-wave. 

By  the  form  of  a  sound-wave,  we  mean  the  state  of  rarefac- 
tion and  compression  in  its  phases,  or  rather,  the  form  of  the 
curve  which  would  represent  this  state  of  rarefaction  and  com- 
pression. Figure  131  shows  the  form  of  the  sound-wave  that 


132  NATURAL    PHILOSOPHY. 

would  be  produced  by  the  fundamental  vibration  of  a  tuning- 
fork.  This  curve  represents  a  simple  wave-form.  The  mole- 
cules in  this  wave  have  a  simple  pendulous  vibration. 

When  the  fundamental  and  harmonic  vibrations  coexist  in  a 
body,  as  in  a  vibrating  string,  the  motion  of  each  point  of  the 
body  is  the  resultant  of  the  motions  which  each  kind  of  vibra- 
tion alone  would  give  it.  This  is  usually  very  far  from  a  simple 
pendulous  vibration.  Figure  132  shows  the  form  of  the  sound- 
wave produced  by  the  vibration  of  the  violin  string.  This  is  a 
compound  wave-form.  The  vibration  of  the  molecules  in  this 
wave-form  is  also  compound;  that  is,  it  is  the  resultant  of  the 
combination  of  two  or  more  kinds  of  vibration. 

Fig.  132. 


171.  Pitch  of  Sound. — The  loudness,  or  intensity,  of 
sound  depends  upon  the  energy  of  the  molecular  vibrations 
in  the  sound-waves.  In  the  curve  representing  the  form 
of  the  sound-wave,  the  loudness  would  be  represented  by 
the  height  of  the  curves,  or  the  amplitude  of  the  wave. 

The///^  of  sound  depends  upon  the  rate  at  which  the 
pulsations  of  sound  strike  upon  the  drum  of  the  ear,  or 
upon  the  length  of  the  sound-waves.  The  length  of  the 
sound-waves  depends  chiefly  upon  the  rate  of  vibration  of 
the  sonorous  body. 

Two  sounds  are  said  to  be  in  unison  when  the  rate  of 
vibration  is  the  same ;  to  form  an  octave,  when  their 
rates  of  vibration  are  as  2  to  i  ;  &  fifth,  when  their  rates 
of  vibration  are  as  3  to  2  ;  a  fourth,  when  their  rates  of 
vibration  are  as  4  to  3  ;  and  a  major  third,  when  their  rates 
of  vibration  are  as  5  to  4. 

In  the  lowest  note  of  the  organ  there  are  16^2  vibrations 
a  second.  In  the  lowest  note  of  the  piano  there  are  33 
vibrations  a  second,  and  in  the  highest  note  4224;  giving 
a  range  of  7  octaves.  In  the  highest  note  ever  heard  in 


NATURAL    PHILOSOPHY.  133 

an  orchestra,  there  are  4752  vibrations  a  second.  This 
note  is  given  by  the  piccolo  flute.  In  the  shrillest  sounds 
that  are  audible  there  are  about  32,000  vibrations  a  second, 
the  upper  limit  of  audibility  varying  with  different  persons. 
The  voice  of  ordinary  chorus-singers  ranges  from  100  to 
1000  vibrations  a  second,  and  the  extreme  limits  of  the 
human  voice  are  50  and  1500  vibrations  a  second. 

172.  Quality  of  Sound.  — The  quality  of  sound  depends 
upon  the  form  of  the  sound-waves,  that  is,  upon  the  har- 
monic vibrations  which  are  present  with  the  fundamental 
vibration   in   the  sonorous  body.     The  pitch  of  sound  is 
determined  chiefly  by  the  fundamental  note.     Two  sounds 
of  the>same  pitch  may  differ  in  quality,  because  of  differ- 
ences in  their   harmonics.      Fundamental  tones  are  those 
produced  by  the  fundamental  vibration  of  a  sonorous  body  ; 
and  harmonic  tones,  those  produced  by  the  harmonic  vibra- 
tions.    No  two  instruments  or  voices  give  tones  of  the 
same  quality,  though  they  may  be  of  the  same   loudness 
and  pitch. 

The  difference  between  a  noise  and  a  musical  sound  is 
that  the  latter  is  smooth  and  regular,  and  the  former  rough 
and  irregular.  Musical  sounds  are  produced  by  rapid 
periodic  vibrations  of  a  body,  and  noises  by  non-periodic 
vibrations. 

173.  The  Siren.  — The  siren  is  an  instrument  used  for  ascer- 
taining the  rate  of  vibration  in  any  note.      It  is  shown  in  Fig- 
ures 133  and  134,  the  former  being  a  front,  and  the  latter  a  back 
view.     There  is  a  small  wind-chest,  nearly  cylindrical,  having 
its  top  pierced  with  fifteen  holes,  at  equal  distances  round  the 
circumference  of  a  circle.     Just  over  this,  and  nearly  touching 
it.  is  a  movable  circular  plate,  pierced  with  the  same  number  of 
holes  similarly  arranged,  and  so  mounted  that  it  can  rotate  very 
freely  about  its  centre,  carrying  with  it  the  vertical  axis  to  which 
it  is  attached.     This  rotation   is  effected  by  the  action  of  the 
wind,   which   enters  the  wind-chest  from  below,  and   escapes 
through  the  holes.     The  form  of  the  holes  is  shown  by  the  sec- 


134  NATURAL   PHILOSOPHY. 

tion  in  Figure  134.  They  do  not  pass  perpendicularly  through 
the  plates,  but  slope  contrary  ways,  so  that  the  air  when  forced 
through  the  holes  in  the  lower  plate  strikes  against  one  side  of 
the  holes  in  the  upper  plate,  and  thus  blows  it  around  in  a  definite 
direction.  The  instrument  is  driven  by  means  of  the  bellows. 
As  the  rotation  of  one  plate  upon  the  other  causes  the  holes  to 
be  alternately  opened  and  closed,  the  wind  escapes  in  succes- 
sive puffs,  whose  frequency  depends  upon  the  rate  of  rotation. 
Hence  a  note  is  emitted  which  rises  in  pitch  as  the  rotation  be- 
comes more  rapid.  The  siren  will  sound  under  water,  if  water 

Fig-  133-  Fig.  134. 


is  forced  through  it  instead  of  air ;  and  it  was  from  this  circum- 
stance that  it  derived  its  name. 

In  each  revolution  the  fifteen  holes  in  the  upper  plate  come 
opposite  to  those  in  the  lower  fifteen  times,  and  allow  the 
compressed  air  in  the  wind-chest  to  escape,  while  in  the  inter- 
vening positions  its  escape  is  almost  entirely  prevented.  Each 
revolution  thus  gives  rise  to  fifteen  vibrations  ;  and  in  order  to 
know  the  number  of  vibrations  corresponding  to  the  note  emitted, 
it  is  only  necessary  to  have  a  means  of  counting  the  revolutions. 

This  is  furnished  by  a  counter,  which  is  represented  in  Fig- 
ure 134.  The  revolving  axis  carries  an  endless  screw,  driving  a 
wheel  of  100  teeth,  whose  axis  carries  a  hand  traversing  a  dial 
marked  with  100  divisions.  Each  revolution  of  the  perforated 


NATURAL   PHILOSOPHY.  13$ 

plate  causes  this  hand  to  advance  one  division.  A  second  toothed 
wheel  is  driven  intermittently  by  the  first,  advancing  suddenly 
one  tooth  whenever  the  hand  belonging  to  the  first  wheel  passes 
the  zero  of  its  scale.  This  second  wheel  also  carries  a  hand 
traversing  a  second  dial ;  and  at  each  of  the  sudden  movements 
just  described  this  hand  advances  one  division.  Each  divis- 
ion, accordingly,  indicates  100  revolutions  of  the  perforated 
plate,  or  1500  vibrations.  By  pushing  in  one  of  the  two  but- 
tons which  are  shown,  one  on  each  side  of  the  box  containing 
the  toothed  wheels,  we  can  instantaneously  connect  or  discon- 
nect the  endless  screw  and  the  first  toothed  wheel. 

In  order  to  determine  the  number  of  vibrations  correspond- 
ing to  any  given  sound  which  we  have  the  power  of  maintaining 
steadily,  we  fix  the  siren  on  the  bellows,  the  screw  and  wheel 
being  disconnected,  and  drive  the  siren  until  the  note  which  it 
emits  is  judged  to  be  in  unison  with  the  given  note.  We  then, 
either  by  regulating  the  pressure  of  the  wind,  or  by  employ- 
ing the  finger  to  press  with  more  or  less  friction  against  the 
revolving  axis,  contrive  to  keep  the  note  of  the  siren  constant 
for  a  measured  interval  of  time,  which  we  observe  by  a  watch. 
At  the  commencement  of  the  interval  we  suddenly  connect  the 
screw  and  toothed  wheel,  and  at  its  termination  we  suddenly 
disconnect  them,  having  taken  care  to  keep  the  siren  in  unison 
with  the  given  sound  during  the  interval. 

The  number  of  vibrations  indicated  on  the  dials  for  the  inter- 
val (ascertained  from  the  difference  of  readings  at  the  beginning 
and  end  of  it),  divided  by  the  number  of  seconds  in  the  interval, 
will  give  the  rate  of  vibration  per  second. 

173.  The  Composition  of  Waves. — The  following  account 
of  the  composition  of  various  systems  of  waves  is  from  Helm- 
holtz:  — 

"  If  a  point  of  the  surface  of  water  is  agitated  by  a  stone 
thrown  upon  it,  the  agitation  is  propagated  in  rings  of  waves  over 
the  surface  to  more  and  more  distant  points.  Now,  throw  two 
stones  at  the  same  time  upon  different  points  of  the  surface, 
thus  producing  two  centres  of  agitation.  Each  will  give  rise  to 
a  separate  ring  of  waves,  and  the  two  rings  gradually  expanding 
will  finally  meet.  Where  the  waves  thus  come  together,  the  water 
will  be  set  in  motion  by  both  kinds  of  agitation  at  the  same  time  •, 


136  NATURAL   PHILOSOPHY. 

but  this  in  no  wise  prevents  both  series  of  waves  from  advancing 
further  over  the  surface,  just  as  if  each  were  alone  present  and 
the  other  had  no  existence  at  all.  As  they  proceed,  those  parts 
of  both  rings  which  had  just  coincided  again  appear  separate  and 
unaltered  in  form.  These  little  waves,  caused  by  throwing  in 
stones,  may  be  accompanied  by  other  kinds  of  waves,  such  as 
those  due  to  the  wind  or  a  passing  steamboat.  Our  circles  of 
waves  will  spread  out  over  the  water  thus  agitated,  with  the 
same  quiet  regularity  as  they  did  upon  the  calm  surface.  Neither 
will  the  greater  waves  be  essentially  disturbed  by  the  less,  nor 
the  less  by  the  greater,  provided  the  waves  never  break  ;  if  that 
happened,  their  regular  course  would  of  course  be  impeded. 

"Indeed,  it  is  seldom  possible  to  survey  a  large  surface  of 
water  from  a  high  point  of  sight  without  perceiving  a  great  mul- 
titude of  different  systems  of  waves,  mutually  overtopping  and 
crossing  each  other.  This  is  best  seen  on  the  surface  of  the  sea, 
viewed  from  a  lofty  cliff,  when  there  is  a  lull  after  a  stiff  breeze. 
We  first  see  the  great  waves,  advancing  in  far-stretching  ranks 
from  the  blue  distance,  here  and  there  more  clearly  marked  out 
by  their  white  foaming  crests,  and  following  one  another  at  regu- 
lar intervals  towards  the  shore.  From  the  shore  they  rebound, 
in  different  directions  according  to  its  sinuosities,  and  cut  ob- 
liquely across  the  advancing  waves.  A  passing  steamboat  forms 
its  own  wedge-shaped  wake  of  waves,  or  a  bird  darting  on  a  fish 
excites  a  small  circular  system.  The  eye  of  the  spectator  is 
easily  able  to  pursue  each  one  of  these  different  trains  of  waves, 
great  and  small,  wide  and  narrow,  straight  and  curved,  and 
observe  how  each  passes  over  the  surface,  as  undisturbedly  as  if 
the  water  over  which  it  flits  were  not  agitated  at  the  same  time 
by  other  motions  and  forces.  I  must  own  that  whenever  I  at- 
tentively observe  this  spectacle,  it  awakens  in  me  a  peculiar  kind 
of  intellectual  pleasure,  because  it  bares  to  the  bodily  eye  what 
the  mind's  eye  grasps  only  by  the  help  of  a  long  series  of  com- 
plicated conclusions  for  the  waves  of  the  invisible  atmospheric 
ocean. 

"  We  have  to  imagine  a  perfectly  similar  spectacle  proceeding 
in  the  interior  of  a  ball-room,  for  instance.  Here  we  have  a  num- 
ber of  musical  instruments  in  action,  speaking  men  and  women, 
rustling  garments,  gliding  feet,  clinking  glasses,  and  so  on.  All 


NATURAL    PHILOSOPHY.  137 

these  causes  give  rise  to  systems  of  waves,  which  dart  through 
the  mass  of  air  in  the  room,  are  reflected  from  its  walls,  return, 
strike  the  opposite  wall,  are  again  reflected,  and  so  on,  till  they 
die  out.  We  have  to  imagine  that  from  the  mouths  of  men  and 
from  the  deeper  musical  instruments  there  proceed  waves  of  from 
8  to  12  feet  in  length,  from  the  lips  of  the  women  waves  of  2  to  4 
feet  in  length,  from  the  rustling  of  the  dresses  a  fine  small 
crumple  of  waves,  and  so  on  ;  in  short,  a  tumbled  entanglement 
of  the  most  different  kinds  of  motion,  complicated  beyond 
conception. 

"And  yet,  as  the  ear  is  able  to  distinguish  all  the  separate 
constituent  parts  of  this  confused  whole,  we  are  forced  to  con- 
clude that  all  these  different  systems  of  waves  coexist  in  the 
mass  of  air,  and  leave  one  another  mutually  undisturbed.  But 
how  is  it  possible  for  them  to  coexist,  since  every  individual  train 
of  waves  has  at  any  particular  point  in  the  mass  of  air  its  own 
particular  degree  of  condensation  and  rarefaction,  which  deter- 
mines the  velocity  of  the  particles  of  air  to  this  side  or  that?  It 
is  evident  that  at  each  point  in  the  mass  of  air,  at  each  instant 
of  time,  there  can  be  only  one  single  degree  of  condensation, 
and  that  the  particles  of  air  can  be  moving  with  only  one  single 
kind  of  motion,  having  only  one  single  amount  of  velocity,  and 
passing  in  only  one  single  direction. 

"What  happens  under  such  circumstances  is  seen  directly  by 
the  eye  in  the  waves  of  water.  If  where  the  water  shows  large 
waves  we  throw  a  stone  in,  the  waves  thus  caused  will,  so  to 
speak,  cut  into  the  larger  moving  surface  ;  and  this  surface  will 
be  partly  raised  and  partly  depressed  by  the  new  waves  in  such  a 
way  that  the  fresh  crests  of  the  rings  will  rise  just  as  much  above, 
and  the  troughs  sink  just  as  much  below,  the  curved  surfaces  of 
the  previous  larger  waves  as  they  would  have  risen  above  cr 
sunk  below  the  horizontal  surface  of  calm  water.  Hence,  where 
a  crest  of  the  smaller  system  of  rings  of  waves  comes  upon  a 
crest  of  the  greater  system,  the  surface  of  the  water  is  raised 
by  the  sum  of  the  two  heights;  and  where  a  trough  of  the 
former  coincides  with  a  trough  of  the  latter,  the  surface  is  de- 
pressed by  the  sum  of  the  two  depths.  This  may  be  expressed 
more  briefly  if  we  consider  the  heights  of  the  crests  above  the 
level  of  the  surface  at  rest  as  positive  magnitudes,  and  the 


138  NATURAL   PHILOSOPHY. 

depths  of  the  troughs  as  negative  magnitudes,  and  then  form 
the  so-called  algebraical  sum  of  these  positive  and  negative 
magnitudes,  in  which  case,  as  is  well  known,  two  positive  mag- 
nitudes (heights  of  crests)  must  be  added,  and  similarly  for  two 
negative  magnitudes  (depths  of  troughs)  ;  but  when  both  nega- 
tive and  positive  concur,  one  is  to  be  subtracted  from  the  other. 
Performing  the  addition  then  in  this  algebraical  sense,  we  can 
express  our  description  of  the  surface  of  the  water  on  which 
two  systems  of  waves  concur  in  the  following  simple  manner : 
The  distance  of  the  surface  of  the  water  at  any  point  from  its 
position  of  rest  is  at  any  moment  equal  to  the  sum  of  the  dis- 
tances at  which  it  would  have  stood  had  each  wave  acted  sepa- 
rately at  the  same  place  and  at  the  same  time.  Hence,  although 
the  surface  of  the  water  at  any  instant  of  time  can  assume  only 
one  single  form,  while  each  of  two  different  systems  of  waves 
simultaneously  attempts  to  impress  its  own  shape  upon  it,  we  are 
able  to  suppose  in  the  above  sense  that  the  two  systems  coexist 
and  are  superimposed,  by  considering  the  actual  elevations  and 
depressions  of  the  surface  to  be  suitably  separated  into  two 
parts,  each  of  which  belongs  to  one  of  the  systems  alone. 

"  In  the  same  sense,  then,  there  is  also  a  superimposition  of 
different  systems  of  sound  in  the  air.  By  each  train  of  waves 
of  sound,  the  density  of  the  air,  and  the  velocity  and  position  of 
the  particles  of  air,  are  temporarily  altered.  There  are  places  in 
the  wave  of  sound  comparable  with  the  crests  of  the  waves  of 
water,  in  which  the  quantity  of  the  air  is  increased,  and  the  air, 
not  having  free  space  to  escape,  is  condensed ;  and  other  places 
in  the  mass  of  air,  comparable  to  the  troughs  of  the  waves  of 
water,  having  a  diminished  quantity  of  air,  and  hence  diminished 
density.  It  is  true  that  two  different  degrees  of  density,  pro- 
duced by  two  different  systems  of  waves,  cannot  coexist  in  the 
same  place  at  the  same  time  ;  nevertheless,  the  condensations 
and  rarefactions  of  the  air  can  be  (algebraically)  added,  ex- 
actly as  the  elevations  and  depressions  of  the  surface  of  the  water 
in  the  former  case.  Where  two  condensations  are  added  we 
obtain  increased  condensation,  where  two  rarefactions  are  added 
we  have  increased  rarefaction  ;  while,  if  a  condensation  and  rare- 
faction concur,  they  mutually,  in  whole  or  in  part,  destroy  or 
neutralize  each  other. 


NATURAL   PHILOSOPHY.  139 

"  The  displacements  of  the  particles  of  air  are  compounded 
in  a  similar  manner.  For  the  magnitude  of  these  displace- 
ments as  well  as  for  the  velocities  with  which  the  particles 
of  air  move  outward  and  inward,  the  same  (algebraical)  addi- 
tion holds  good  as  for  the  crests  and  troughs  of  waves  in 
water. 

"  Hence,  when  several  resonant  bodies  in  the  surrounding 
atmosphere  simultaneously  excite  different  systems  of  waves  of 
sound,  the  changes  of  density  of  the  air,  and  the  displacements 
and  velocities  of  the  particles  of  the  air  within  the  passages  of  the 
ear,  are  each  equal  to  the  (algebraical)  sum  of  the  corresponding 
changes  of  density,  displacements,  and  velocities  which  each 
system  of  waves  would  have  separately  produced,  if  it  had  acted 
independently ;  and  in  this  sense  we  can  say  that  all  the  sepa- 
rate vibrations  which  separate  waves  of  sound  would  have 
produced,  coexist  undisturbed  at  the  same  time  within  the 
passages  of  our  ear." 

174.  Interference  of  Sound.  —  When  two  equal  water- 
waves  meet  in  the  same  phase,  namely,  so  that  the  crest 
of  one  coincides  with  the  crest  of  the  other,  and  the  hollow 
of  one  with  the  hollow  of  the  other,  their  combination 
produces  at  the  point  of  meeting  a  wave  of  double  the 
height.  Were  the  two  waves  to  meet  in  opposite  phases, 
that  is,  so  that  the  hollow  of  one  coincides  with  the  crest 
of  the  other,  their  combination  would  leave  the  surface  of 
the  water  undisturbed.  There  would  be  neither  depression 
nor  elevation. 

In  a  similar  way,  when  two  equal  sound-waves  meet  in 
the  same  phase,  their  combination  would  produce  at  the 
point  of  meeting  a  wave  of  twice  the  degree  of  condensa- 
tion and  rarefaction  of  either  of  the  component  waves. 
Were  the  two  waves  to  meet  in  opposite  phases,  the  air  would 
be  undisturbed  at  the  place  of  meeting.  There  would  be 
neither  condensation  nor  rarefaction.  An  ear  at  the  point 
of  meeting  of  the  waves  in  the  first  case  would  hear  a  sound 
much  louder  than  that  conveyed  by  either  sound-wave 


14°  NATURAL    PHILOSOPHY. 

alone ;  while  in  the  second  case  it  would  hear  no  sound  at 
all.  The  meeting  of  two  sound-waves  so  as  to  neutralize 
each  other  is  called  the  interference  of  sound. 

Strike  a  tuning-fork  so  as  to  throw  its  prongs  into  vibra- 
tion, and  hold  it  vertically  near  the  ear,  and  turn  it  slowly 
around  so  as  to  bring  the  sides,  the  edges,  and  the  corners 
of  the  prongs  successively  towards  the  ear.  Four  posi- 
tions of  the  fork  will  be  found  in  which  its  sound  will  be 
inaudible.  Let  a  and  b  (Figure  135) 
be  the  ends  of  the  prongs  of  a  tun- 
ing-fork  in  vibration.  The  sound  of 
the  fork  is  inaudible  when  the  ear  is 
on  any  one  of  the  dotted  lines.  As 
the  prongs  vibrate,  each  develops  a 
series  of  waves,  and  along  the  dotted 

/  V       lines  these  two  sets  of  waves  will  be 

^/  *x 

v-  of  equal  intensity  and  in  opposite 
phases.  Hence  along  these  lines  the  two  sets  of  waves 
neutralize  each  other,  and  silence  results  from  the  combi- 
nation of  two  sounds. 

175.  Musical  Beats.  —  Suppose  two  tuning-forks,  slightly 
different  in  pitch,  to  be  started  together,  and  suppose  the 
prongs  of  both  to  be  moving  forward  at  the  same  time  ; 
they  will  start  waves  of  the  same  phase  which  will  coincide 
with  and  intensify  each  other.  The  fork  having  the  higher 
pitch  will,  however,  immediately  begin  to  gain  on  the 
other,  and  the  coincidence  of  the  waves  will  be  less  and 
less  perfect  until  this  fork  has  gained  half  a  vibration  on 
the  other.  The  prongs  of  the  two  forks  will  now  be  mov- 
ing in  opposite  directions  at  the  same  time,  and  the  waves 
started  by  the  two  forks  will  be  in  opposition,  and  will 
neutralize  each  other  wholly  or  in  part.  After  this  there 
will  again  be  partial  coincidence  of  the  waves,  and  the 
degree  of  coincidence  will  increase  till  the  higher  fork  has 
gained  a  whole  vibration  on  the  lower  one,  when  the  coin- 


NATURAL    PHILOSOPHY.  14! 

cidence  will  again  be  complete.  When  two  such  forks  are 
started  together,  the  sound  gradually  dies  away  till  it 
becomes  nearly  or  altogether  inaudible ;  it  then  swells  out 
loudly,  and  gradually  dies  away  again  at  regular  intervals. 
These  gradual  risings  and  fallings  in  the  intensity  of  sound 
are  called  beats. 

These  beats  occur  whenever  two  sounds  of  nearly  the 
same  pitch  are  produced  together.  The  rate  of  beating 
will  be  equal  to  the  difference  of  the  rate  of  vibration  in 
the  two  sonorous  bodies.  If  one  of  the  bodies  gains  one 
vibration  a  second  on  the  other,  the  sounds  will  beat  once 
a  second  ;  if  it  gains  two  vibrations  a  second,  the  sounds 
will  beat  twice  a  second ;  and  so  on. 

The  less  the  sounds  differ  in  pitch  the  slower  the  beats, 
and  the  more  they  differ  in  pitch  the  more  rapid  the  beats. 

Even  after  the  beats  become  too  rapid  to  be  distin- 
guished by  the  ear,  they  give  a  disagreeable  roughness  to 
the  sound.  According  to  Helmholtz,  dissonance  is  en- 
tirely due  to  the  roughness  produced  by  a  rapid  succession 
of  beats,  which  take  place  between  either  the  fundamental 
tones  or  the  harmonics  which  are  present  in  the  two 
sounds. 

C.    RESONANCE. 

176.  Sympathetic  Vibrations  of  Tuning- Forks.  —  Take 
two  tuning-forks  of  exactly  the  same  pitch,  cause  one  of 
them  to  vibrate,  and  hold  it  near  the  other  without  touch- 
ing it.  The  second  fork  will  soon  begin  to  vibrate,  and 
will  emit  a  distinctly  audible  sound  after  the  first  has  been 
stopped.  The  second  fork  will  not  be  started  by  the  first 
unless  the  two  are  of  exactly  the  same  pitch,  as  may  be 
shown  by  sticking  a  little  pellet  of  wax  to  the  prong  of  one 
of  the  forks  so  as  to  diminish  its  rate  of  vibration.  Vibra- 
tions started  in  one  body  by  the  vibrations  of  another  are 
called  sympathetic  vibrations.  The  production  of  sound 
by  sympathetic  vibrations  is  called  resonance. 


142  NATURAL    PHILOSOPHY. 

The  vibrations  are  communicated  from  one  fork  to  the 
other  by  means  of  the  air.  The  vibrations  of  the  first  fork 
produce  condensations  and  rarefactions  in  the  air  which 
succeed  each  other  at  the  rate  at  which  the  fork  is  vibrat- 
ing. The  number  of  condensations  which  would  pass  any 
point  in  the  room  in  a  second  is  exactly  equal  to  the  num- 
ber of  vibrations  executed  by  the  fork  in  a  second.  In 
the  condensations  the  pressure  of  the  air  is  increased,  and 
in  the  rarefactions  it  is  diminished.  Each  condensation 
as  it  passes  the  prong  of  the  second  fork  gives  it  a  little 
push.  As  the  second  fork  vibrates  at  exactly  the  same 
rate  as  the  first,  each  condensation  arrives  in  time  to  push 
the  prong  just  as  it  is  ready  to  move  forward  of  itself. 
Hence  the  prong  is  always  pushed  in  the  direction  in 
which  it  is  moving.  The  push  of  one  condensation  moves 
the  prong  but  little,  but  the  pushes  are  so  timed  that  each 
moves  it  a  little  farther  than  the  last,  until  the  fork  is 
made  to  vibrate  strongly.  The  elasticity  and  inertia  of 
the  fork  are  such  that  it  still  continues  to  vibrate  when  it 
has  been  started,  even  though  the  first  fork  is  stopped. 

When  the  second  fork  cannot  vibrate  at  the  same  rate 
as  the  first,  the  condensation  will  sometimes  push  in  the 
direction  in  which  the  prong  is  moving  and  sometimes  in 
the  opposite  direction.  Hence  one  push  will  neutralize 
the  effect  of  another  instead  of  augmenting  it. 

177.  Sympathetic  Vibrations  of  Strings.  —  If  a  piano  is 
opened  and  one  of  the  keys  gently  depressed  so  as  to  raise 
the  damper  without  striking  the  string  with  the  hammer, 
and  the  note  of  the  string  is  then  sung  over  the  piano,  the 
string  will  begin  to  vibrate  and  will  emit  an  audible  sound 
for  a  little  time  after  the  voice  ceases.  It  is  only  neces- 
sary to  hit  the  pitch  of  a  string  accurately  and  to  sustain 
the  note  sufficiently.  Sympathetic  vibrations  are  started 
more  readily  in  strings  than  in  tuning-forks,  but  they  are 
less  persistent.  They  very  soon  die  away  after  the  excit- 


NATURAL  PHILOSOPHY.  143 

ing  sound  ceases.  Strings  may  be  thrown  into  vibration 
by  their  harmonic  notes  as  well  as  by  their  fundamental 
notes. 

178.  Sympathetic  Vibrations  of  Thin  Membranes.  —  Thin 
membranes  when  stretched  are  very  readily  thrown  into 
sympathetic  vibration,  but  their  vibrations  stop  promptly 
when  the  exciting  sound  ceases.      Owing  to  the  facility 
with  which   they  break  up  into  vibrating  segments,  they 
respond  readily  to  all  rates  of  vibration.    The  same  is  true 
of  thin  metallic  plates. 

179.  Sympathetic    Vibrations  of  Masses  of  Air.  —  If   a 
vibrating  tuning-fork  is  held  at  the  end  of  a  tube  an  inch 
and  a  half  or  two  inches  in  diameter,  the  sound  of  the  fork 
will  be  powerfully  reinforced,  provided  the  tube  is  of  suit- 
able length.     The  suitable  length  for  a  tube  open  at  both 
ends  is  one  half  of  the  length  of  the  wave  produced  by  the 
fork.     A  tube  closed  at  one  end  resounds  most  powerfully 
when  its  length  is  one  quarter  of  the  length  of  the  wave 
produced  by  the  fork.     The  column  of  air  in  the  tube  is 
thrown  into  powerful  sympathetic  vibration  by  the  fork, 
and   these  vibrations   greatly  augment  the  sound.      The 
moment  the  fork  is  stopped  the  resonance  ceases. 

-Columns  of  air  may  also  be  thrown  into  sympathetic 
vibration  by  their  harmonic  vibrations.  By  altering  the 
shape  of  the  tube  it  may  be  made  to  reinforce  certain  har- 
monics more  powerfully  than  others,  and  so  change  the 
quality  of  the  exciting  sound. 

1 80.  Sounding  Boards  and  Boxes.  —  The   sound   of   a 
tuning-fork  is  feeble  unless  reinforced  by  a  resonant  case 
of  suitable  dimensions  to  which  the  fork  is  fixed.     Such  a 
resonant  case  is  called  a  sounding-box. 

Thin  pieces  of  dry  straight-grained  pine,  such  as  are 
employed  for  the  faces  of  violins  and  the  sounding-boards 
of  pianos,  are  capable  of  vibrating  more  or  less  freely,  in 
any  period  lying  between  certain  wide  limits.  They  are 


144  NATURAL  PHILOSOPHY. 

accordingly  set  in  vibration  by  all  the  notes  of  their  rt 
spective  instruments  ;  and  by  the  large  surface  with  whicl 
they  act  upon  the  air,  they  contribute  in  a  very  high  degret 
to  increase  the  sonorous  effect.  All  stringed  instruments 
are  provided  with  sounding-boards ;  and  their  quality 
mainly  depends  on  the  greater  or  less  readiness  with  which 
these  respond  to  the  vibrations  of  the  strings. 

D.   MUSICAL  INSTRUMENTS. 

181.  Stringed  Instruments.  —  In  one  class  of  musical  in- 
struments the  notes  are  produced  by  the  transverse  vibra- 
tions of  strings.  These  instruments  are  called  stringed 
instruments.  The  rate  at  which  a  string  vibrates  depends 
upon  its  length,  its  weight,  and  its  tension.  The  shorter, 
the  tighter,  and  the  lighter  a  string,  the  faster  it  vibrates. 
Strings  may  be  thrown  into  transverse  vibration  by  draw- 
ing a  rosined  bow  across  them,  as  in  the  case  of  the  violin; 
or  by  plucking  them  with  the  finger,  as  in  the  case  of  the 
harp ;  or  by  striking  them  with  a  hammer,  as  in  the  case 
of  the  piano. 

In  the  piano  there  is  a  string  for  every  note.  In  the 
violin  and  similar  instruments,  several  notes  are  obtained 
from  the  same  string  by  fingering  it  so  as  to  change  its 
length  and  tension. 

Fig.  r36. 


182.  The  Sonometer.  —  The  sonometer  is  an  instrument 
for  investigating  the  laws  of  the  vibration  of  strings.  It 
is  shown  in  Figure  136.  It  consists  essentially  of  a  string 


NATURAL   PHILOSOPHY.  145 

or  wire  stretched  over  a  sounding-box  by  means  of  a 
weight.  One  end  of  the  string  is  secured  to  a  fixed  point 
at  one  end  of  the  sounding-box ;  the  other  end  passes 
over  a  pulley,  and  carries  weights  which  can  be  altered  at 
pleasure.  Near  the  two  ends  of  the  box  are  two  fixed 
bridges,  over  which  the  cord  passes.  There  is  also  a 
movable  bridge,  which  can  be  employed  for  altering  the 
length  of  the  vibrating  portion. 

183.  Wind    Instruments.  —  In    wind    instruments    the 
notes  are  produced  by  the  longitudinal  vibrations  of  col- 
umns of   air  enclosed   in   pipes.     The   rate   of   vibration 
depends  upon  the  length  of  the  column,  and  upon  whether 
the  pipe  is  open  or  is  closed.     The  shorter  a  column  of 
air  the  faster  it  vibrates,  and   the   air   in   an   open  tube 
vibrates  twice  as  fast  as  that  in  a  closed  pipe  of  the  same 
length.     This  is  because  the  air  in  a  closed  pipe  vibrates 
as  a  whole,  while  that  in  an  open  pipe  vibrates  in  two  seg- 
ments, there  being  a  stationary  point  or  node  at  the  centre 
of  the  pipe.     In   an  organ  there  are  as  many  pipes  as 
notes,  only  one  note  being  obtained  from  each  pipe.     In 
the  case  of  the  flute  and  similar  wind  instruments,  several 
notes  are  obtained  from  one  pipe  by  opening  and  closing 
the  holes  at  the  side  .of  the  pipe  so  as  to  alter  the  length 
of  the  vibrating  column  of  air,  and  by  altering  the  strength 
of  the  blast  so  as  to  change  from  the  fundamental  note  of 
the  pipe  to  one  or  other  of  its  harmonics. 

In  all  wind  instruments  the  pipe  is  made  to  speak  by 
resonance.  The  sympathetic  vibrations  in  the  pipe  are 
sometimes  started  by  the  vibrations  of  the  lips,  as  in  the 
case  of  the  trumpet ;  or  by  the  vibrations  of  a  spring  called 
a  reed,  as  in  the  case  of  the  clarionet ;  or  by  the  flutter  of 
a  jet  of  air  when  blown  against  a  sharp  edge,  as  in  the 
case  of  the  flute. 

184.  Organ  Pipes.  —  Organ  pipes  are  made  of  wood  or 
metal,  and   they  are   made  to   speak   either   by  blowing 


i46 


NATURAL   PHILOSOPHY. 


against  a  sharp  edge  so  as  to  produce  a  flutter,  or  by  blow- 
ing against  a  spring  so  as  to  throw  it  into  vibration.  Pipes 
which  are  made  to  speak  in  the  first  way  are  called  flue- 
pipes  ;  and  those  made  to  speak  in  the  second  way,  reed- 
pipes.  Pipes  closed  at  one  end  are  called  stopped  pipes  ; 
and  those  open  at  both  ends,  open  pipes. 

Fig.  137-  Fig.  138. 


These  pipes  are  shown  in  Figures  137  and  138.  The 
air  passes  from  the  bellows  through  the  tube  P  into  a 
chamber,  which  is  closed  at  the  top  except  the  narrow 
slit  z.  The  air  compressed  in  the  chamber  passes  through 
this  slit  in  a  thin  sheet,  which  breaks  against  a  sharp  edge 
a,  and  there  produces  a  flutter.  The  space  between  the 
edge  a  and  the  slit  below  is  called  the  mouth  of  the  pipe. 


NATURAL    PHILOSOPHY. 


The  metal  reed  commonly  used  in  organ  pipes  is  shown  in 
Figure   139.     It  consists  of  a  long  strip  of  flexible  metal 

Fig.  139- 


V  V,  placed  in  a  rectangular  opening,  through  which  the 
current  of  air  enters  the  pipe.     As  soon  as  the  air  begins 

Fig.  140. 


to  enter  the  pipe,  the  force  of  the  blast  bends  down  the 
spring  of  the  reed  so  as  to  close  the  opening.     The  elas- 


148  NATURAL    PHILOSOPHY. 

ticity  of  the  reed  causes  it  to  fly  back  at  once,  so  as  to  open 
the  pipe  and  allow  the  air  to  enter  again.  It  thus  breaks 
up  the  current  of  air  into  a  regular  succession  of  little 
puffs. 

The  way  in  which  the  reed  and  pipe  are  connected 
is  shown  in  Plgure  140.  The  reed  is  placed  within  the 
chamber  Kt  into  which  air  is  forced  through  the  tube  at 
the  bottom.  Tis  a  conical  pipe  of  metal,  the  opening  of 
which  is  covered  by  the  reed  as  already  explained.  The 
wire  b  r  is  used  to  lengthen  or  shorten  the  reed,  and  thus 
to  vary  its  rate  of  vibration. 

The  quality  of  the  sound  of  an  organ  pipe  depends 
chiefly  upon  the  shape  of  the  pipe,  which  causes  it  to 
reinforce  more  or  less  powerfully  certain  of  the  harmonics 
which  are  present  with  the  fundamental  note. 

185.  The   Organ  of  the  Human    Voice. — The  organ  of 
voice  in  man  is  situated  at  the  top  of  the  windpipe,  or 
trachea,  which  is  the  tube  through  which  the  air  is  blown 
from  the  lungs.     A  pair  of  elastic  bands,  called  the  vocal 
chords,   stretched  across  the  top  of   the  windpipe   so   as 
nearly  to  close  it,  form  a  double  reed.     When  the  air  is 
forced  from  the  lungs  through  the  slit  between  the  chords, 
these  are  made  to  vibrate.     By  changes  in  their  tension, 
their  rate  of  vibration  is  varied,  and  the  sound  raised  or 
lowered  in  pitch.     The  cavity  of  the  mouth  and  nose  acts 
as  a  resonant  tube,  and  by  altering  the  shape  of  this  cavity 
we  can  give  greater  prominence  either  to  the  fundamental 
note  of  the  vocal  chords  or  to  any  of  their  harmonics. 

1 86.  Singing  Flames.  —  The  air  in  an  open  tube  may  be 
made  to  give  a  sound  by  means  of  a  luminous  jet  of  hydro- 
gen, coal  gas,  etc.     When  a  glass  tube  about  twelve  inches 
long  is  held  over  a  lighted  jet  of  hydrogen  (Figure  141), 
a  note  is  produced,  which,  if  the  tube  is  in  a  certain  posi- 
tion, is  the  fundamental  note  of  the  tube.     The  current  of 
air   passing  up   through   the  tube  over   the  flame  causes 


NATURAL    PHILOSOPHY.  149 

the  flame  to  flutter,  and  the  air    in   the  tube  reinforces 

some  pulsations  of  this  flutter  by   sympathetic   vibration. 

The  vibration  of  the  column  Fig  I4I 

of  air  in  the  tube  reacts  upon 

the  flame,   and  causes  it   to 

vibrate    more    regularly   and 

more  powerfully.     The   note 

depends    on    the  size  of  the 

flame  and  the  length  of  the 

tube  ;    with  a  long  tube,  by 

varying  the  position  of  the  jet 

in  the  tube,  a  series  of  notes 

in   the  ratio  1:2:3:4:5   is 

obtained. 

If,  while  the  tube  emits  a 
certain  sound,  the  voice  or  the 
siren  is  gradually  raised  to 
the  same  pitch,  as  soon  as  the 

note  is  nearly  in  unison  with  that  of  the  tube,  the  flame 
becomes  agitated,  jumps  up  and  down,  and  is  finally  steady 
when  the  two  sounds  are  in  unison.  If  the  note  of  the 
siren  is  then  gradually  raised,  the  pulsations  again  com- 
mence ;  they  are  the  optical  expressions  of  the  beats  which 
occur  near  perfect  unison.  If,  while  the  jet  burns  in  the 
tube  and  produces  a  note,  the  position  of  the  tube  is 
slightly  altered,  a  point  is  reached  at  which  no  sound  is 
heard.  If  now  the  voice,  or  the  siren,  or  the  tuning-fork 
is  pitched  at  the  note  produced  by  the  jet,  it  begins  to 
sing,  and  continues  to  sing  even  after  the  siren  is  silent. 
A  mere  noise  or  shouting  at  an  incorrect  pitch  affects  the 
flame,  but  does  not  cause  it  to  sing. 

E.   ANALYSIS  OF  SOUND. 

187.    Analysis  of  Sound  by  Resonance.  —  We  have  seen  that 
sound  originates  in  molar  vibrations,  and  that  it  is  propagated 


150  NATURAL    PHILOSOPHY. 

by  waves  chiefly  through  the  air.  Very  few  sounds  are  simple, 
most  sounds  being  composed  of  various  mixtures  of  funda- 
mental and  harmonic  tones.  Most  sound-waves  are  compound. 
Sound-waves  are  compounded  like  water-waves,  but  there  is  one 
essential  difference  between  the  two  cases.  A  compound  water- 
wave  has  but  a  momentary  existence  ;  the  long  waves  move  ovei 
the  surface  of  water  faster  than  the  short  ones.  Hence,  when 
two  sets  of  water-waves  of  different  lengths  unite,  they  quickly 
separate  again,  and  enter  into  new  combinations.  When  two 
sets  of  sound-waves  moving  in  the  same  direction  combine,  the 
combination  is  permanent,  since  long  and  short  waves  traverse 
the  air  at  the  same  rate. 

These  compound  wave-forms  may  be  decomposed  into  their 
constituent  elements  by  means  of  resonance. 

1 88.  The  Analysis  of  Sound  by  the  Resonance  of  Strings.  — 
If  we  raise  the  dampers  of  a  piano,  and  sing  any  one  of  the 
vowels,  A,  E,  O,  and  U,  strongly  over  the  piano,  the  strings 
which  are  capable  of  vibrating  at  the  rate  of  any  of  the  tones  in 
the  vowel  sounds  will  be  thrown  into  sympathetic  vibration. 
When  one  stops  singing  over  the  piano,  the  strings  will,  by  their 
resonance,  give  back  the  vowel  sound.  The  different  strings 
which  were  thrown  into  sympathetic  vibration  produce  by  their 
joint  vibrations  a  compound  wave  of  the  same  form  as  that 
which  left  the  mouth  when  it  uttered  the  vowel.  This  com- 
pound wave  is  first  decomposed  by  the  strings  into  its  constit- 
uent elements,  and  then  these  elements  are  again  recombined  in 
the  new  wave  formed  by  the  vibrating  strings. 

189.    The  Analysis  of  Sound  by  Means  of  Resonators.— 
Kelmholtz  devised  an  instrument  for  the  analysis  of  sound  which 
Fig  ,42t  he  called  a  resonator.     One  of  these 

resonators  is  shown  in  Figure  142.  It 
is  a  hollow  globe  of  thin  brass,  with 
an  opening  at  each  end.  The  larger 
opening  is  for  the  admission  of  sound, 
and  the  smaller  one  for  insertion  into 
the  ear.  The  enclosed  mass  of  air 
has,  like  the  column  of  air  in  an  organ 
pipe,  a  particular  fundamental  note  of 
its  own,  depending  upon  its  size ;  and  whenever  a  note  of  this 


NATURAL    PHILOSOPHY. 


particular  pitch  is  sounded  in  its  neighborhood,  the  enclosed  air 
takes  it  up  and  intensifies  it  by  resonance.  In  order  to  test  the 
presence  or  absence  of  a  particular  harmonic  in  any  sound,  a 
resonator  in  unison  with  the  harmonic  is  applied  to  the  ear.  If 
the  resonator  speaks,  the  harmonic  is  present.  These  instru- 
ments are  usually  constructed  so  as  to  form  a  series  whose 
notes  correspond  to  the  bass  C  of  a  man's  voice  and  its  succes- 
sive harmonics  as  far  as  the  tenth  or  twelfth. 

190.  Koenig's  Manometric  Flames.  —  The  vibrations  of  air 
may  be  transferred  to  gas-flames,  and  thus  rendered  visible. 
The  gas  is  first  conducted  through  a 
tube  to  a  little  gas-chamber,  one  side 
of  which  is  formed  of  a  very  thin  sheet 
of  india-rubber.  The  tube  at  the  end  of 
which  the  gas  is  burned  issues  from  one 
side  of  this  chamber.  One  form  of  the 
chamber  is  shown  in  Figure  143.  The  vertical  line  at  the  centre 
of  the  section  represents  the  stretched  membrane  of  india-rubber. 
The  gas  is  admitted  into  the  little  chamber  to  the  right  of  this 
membrane  through  the  tube  fitted  with  the  stopcock,  and  escapes 
through  the  tube  above,  at  the  end  of 
which  it  is  burned.  The  part  to  the  left 
of  the  membrane  is  for  the  purpose  of 
connecting  the  chamber  to  a  mouth-piece 
or  any  other  apparatus  by  means  of  a 
rubber  tube.  The  vibrations  of  the  air 
being  taken  up  by  the  membrane,  and  thus 
communicated  to  the  gas.  cause  the  flame 
to  leap  up  and  down.  These  oscillations 
of  the  flame  are  so  rapid  and  regular  that, 
when  viewed  directly,  the  flame  appears 
to  be  quite  steady.  Its  altered  condition, 
however,  betrays  itself  by  an  altered  form 
and  color.  But  to  see  the  separate  oscilla- 
tions, the  flames  should  be  viewed  in  a 
rotating  mirror,  in  which  the  flame  at  rest 
appears  to  be  drawn  out  into  a  long  uniform  ribbon,  while 
the  oscillating  flame  appears  as  a  series  of  separate  images  of 
flames.  Figure  144  shows  a  small  mirror,  mounted  so  that  it 


'S2 


NATURAL   PHILOSOPHY. 


may  be  rotated  on  a  vertical  axis  by  the  thumb  and  fingers, 
and  also  shows  the  appearance  of  the  vibrating  flame  as  re- 
flected in  the  rotating  mirror.  Every  change  of  pressure  upon 
the  stretched  membrane  will  be  represented  by  a  different  height 
of  the  reflected  flame.  Figures  145  and  146  show  the  appear- 

Figs.  145,  146. 


ance  of  the  flame  in  the  mirror  on  singing  the  vowel  sound  a  into 
the  mouth-piece  on  the  notes  F  and  C. 

191.  Edison's  Phonograph.  —  In  Edison's  phonograph,  the 
vibrations  of  the  air  are  first  taken  up  by  a  thin  plate  of  metal, 
and  are  then  permanently  registered  on  a  sheet  of  tin-foil. 
This  instrument  is  shown  in  Figure  147.  It  consists  essentially 
of  a  brass  cylinder  C  and  of  a  mouth-piece  F.  On  the  surface  of 
the  cylinder  is  constructed  a  very  accurate  spiral  groove,  the 

Fig.  147. 


threads  of  which  are  about  ^  of  an  inch  apart.  The  cylinder 
is  turned  by  the  crank  D  upon  the  axis  A  B.  On  one  end  of  this 
axis  is  cut  a  thread  of  the  same  fineness  as  the  groove  on  the 
cylinder.  A  sheet  of  tin-foil  is  fastened  smoothly  on  the  surface 
of  the  cylinder. 

An  enlarged' view  of  the  mouth-piece  is  shown  in  Figure  148. 


NATURAL    PHILOSOPHY.  153 

This  mouth-piece  is  supported  on  a  post  G,  and  may  be  moved 
to  and  from  the  cylinder  by  the  lever  H.  At  the  bottom  of  the 
mouth-piece  there  is  an  iron  plate  A  about  T^  of  an  inch  thick. 
Under  this  plate  are  two  pieces  of  rubber  tubing  x  and  x,  which 
separate  it  from  a  spring  supported  by  E,  and  carrying  a  round 
steel  point  P. 

The  point  P  rests  upon  the  tin-foil  on  the  cylinder,  just  over 
the  spiral  groove.  If  the  crank  is  turned,  the  thread  on  the  axis 
causes  the  cylinder  to  move  forward  so  as  to  keep  the  groove 
always  under  the  point.  When  the  iron  plate  is  at  rest,  if  we 

Fig. 


turn  the  crank  the  point  marks  a  spiral  line  of  uniform  depth  on 
the  tin-foil.  If  we  speak  or  sing  into  the  mouth-piece,  the 
vibrations  of  the  air  are  communicated  to  the  iron  plate,  and 
from  this  to  the  point  by  means  of  the  rubber  tube.  If  the  crank 
is  turned  while  speaking  or  singing  into  the  mouth-piece,  the  point 
will  mark  a  clotted  line  on  the  tin-foil.  The  depth  of  the  indenta- 
tions made  by  the  point  in  the  tin-foil  will  exactly  represent  the 
densities  of  the  different  portions  of  the  sound-waves  which 
encounter  the  disc.  The  forms  of  the  sound-waves  are  thus 


154  NATURAL    PHILOSOPHY. 

registered  on  the  tin-foil,  and  may  be  studied  at  leisure  with 
the  microscope. 

If,  after  talking  into  the  mouth-piece,  the  cylinder  is  again  set 
back  to  the  starting-point  and  the  crank  is  then  turned,  the  point 
will  follow  the  indentations  in  the  tin-foil,  and  so  be  compelled  to 
vibrate  exactly  as  it  did  when  it  made  these  indentations  in  the 
foil.  The  vibrations  of  the  point  will  be  communicated  to  the 
thin  iron  plate  by  means  of  the  rubber  tube,  and  by  the  plate  to 
the  air.  Thus  the  words  spoken  into  the  mouth-piece  will  be 
exactly  repeated,  and  by  the  use  of  a  properly  constructed  mouth- 
piece they  are  rendered  audible  throughout  a  large  hall.  By 
resetting  the  cylinder,  they  may  be  repeated  several  times,  though 
more  feebly  each  time  the  foil  is  passed  under  the  point;  the 
indentations  of  the  foil  being  gradually  smoothed  out. 

192.  The  Analysis  of  Sound  by  the  Human  Ear.  — A  sec- 
tion of  the  human  ear  is  shown  in  Figure  149.  In  this  organ  we 
have,  first  of  all,  the  external  opening  of  the  ear,  which  is  closed 
at  the  bottom  by  a  circular  membrane  called  the  tympanum. 
Behind  this  is  the  cavity  called  the  drum  of  the  ear.  This  cav- 
ity is  separated  from  the  space  between  it  and  the  brain  by  a 
bony  partition,  in  which  there  are  two  openings,  the  one  round 
and  the  other  oval.  These  also  are  closed  by  delicate  mem- 
branes. Across  the  cavity  of  the  drum  stretches  a  series  of 
four  little  bones  :  the  first,  called  the  hammer,  is  attached  to  the 
tympanum  ;  the  second,  called  the  anvil,  is  connected  by  a  joint 
with  the  hammer ;  a  third  little  round  bone  connects  the  anvil 
with  the  sttrnepbone,  which  has  its  oval  base  planted  against  the 
membrane  of  the  oval  opening,  almost  covering  it.  Behind  the 
bony  partition,  and  between  it  and  the  brain,  we  have  the  extra- 
ordinary organ  called  the  labyrinth,  which  is  filled  with  water, 
and  over  the  lining  of  which  the  fibres  of  the  auditory  nerve  are 
distributed.  The  tympanum  intercepts  the  vibrations  of  the  air 
in  the  external  ear,  and  transmits  them  through  the  series  of 
bones  in  the  drum  to  the  membrane  which  separates  the  drum 
from  the  labyrinth ;  and  thence  to  the  liquid  within  the  labyrinth 
itself,  which  in  turn  transmits  them  to  the  nerves.  The  trans- 
mission, however,  is  not  direct.  At  a  certain  place  within  the 
labyrinth,  exceedingly  fine  elastic  bristles,  terminating  in  sharp 
points,  grow  up  between  the  nerve  fibres.  These  bristles,  dis- 


NATURAL    PHILOSOPHY.  155 

covered  by  Max  Schultze,  are  exactly  fitted  to  sympathize  with 
those  vibrations  of  the  water  which  correspond  to  their  proper 
periods.  Thrown  thus  into  vibration,  the  bristles  stir  the  nerve 
fibres  which  lie  between  their  roots,  and  the  nerve  transmits  the 
impression  to  the  brain,  and  thus  to  the  mind.  At  another  place 
in  the  labyrinth  we  have  little  crystalline  particles,  called  otoliths, 
—  the  Horsteine  of  the  Germans,  —  embedded  among  the  ner- 
vous filaments,  and  exerting,  when  they  vibrate,  an  intermittent 
pressure  upon  the  adjacent  nerve  fibres.  The  otoliths  probably 
answer  a  different  purpose  from  that  of  the  bristles  of  Schultze. 


Fig.  149- 


They  are  fitted,  by  their  weight,  to  receive  and  prolong  the  vibra- 
tions of  evanescent  sounds  which  might  otherwise  escape  atten- 
tion. The  bristles  of  Schultze,  on  the  contrary,  because  of 
their  extreme  lightness,  would  instantly  yield  up  an  evanescent 
motion,  while  they  are  peculiarly  fitted  for  the  transmis- 
sion of  continuous  vibrations.  Finally,  there  is  in  the  laby- 
rinth a  wonderful  organ,  discovered  by  Corti,  which  is  to  all 
appearance  a  musical  instrument,  with  its  chords  so  stretched  as 
to  receive  vibrations  of  different  periods,  and  transmit  them  to 
the  nerve  filaments  which  traverse  the  organ.  Within  the  ear 
of  man,  and  without  his  knowledge  or  contrivance,  this  lute  of 
3000  strings  has  existed  for  ages,  receiving  the  musk  of  the 
outer  world,  and  rendering  it  fit  for  reception  by  the  brain. 


'56 


NATURAL  PHILOSOPHY. 


Each  musical  tremor  which  falls  upon  this  organ  selects  from  its 
tense  fibres  the  one  appropriate  to  its  own  pitch,  and  throws  that 
fibre  into  sympathetic  vibration.  And  thus,  no  matter  how  com- 
plicated the  motion  of  the  external  air  may  be,  these  micro- 
scopic strings  can  analyze  it,  and  reveal  the  elements  of  which 
it  is  composed. 

Figure  150  is  an  enlarged  view  of  a  portion  of  Corti's  organ. 
Heltnholtz  says  of  this  organ  :  "  The  arches  which  leave  the 
membrane  at  d  and  are  reinserted  at  e,  reaching  their  greatest 
height  between  m  and  0,  are  probably  the  parts  which  are  suited 


for  vibration.  They  are  spun  round  with  innumerable  fibrils, 
among  which  some  nerve  fibres  can  be  recognized,  coming  to 
them  through  the  holes  near  c.  The  transverse  fibres  g,  /z,  /,  k, 
and  the  cells  0,  also  appear  to  belong  to  the  nervous  system. 
There  are  about  three  thousand  arches  similar  to  d,  e,  lying  or- 
derly beside  each  other,  like  the  keys  of  a  piano,  in  the  whole 
length  of  the  partition  of  the  cochlea." 


III. 

HEAT. 
I. 

EFFECTS   OF   HEAT. 
A.   EXPANSION. 

193.  Expansion  of  Solids.  —  As  a  rule,  bodies  expand 
when  heated,  solids  being  the  least  expansible,  liquids 
next,  and  gases  the  most  expansible. 

In  the  case  of  solids  which  have  a  definite  figure,  we 
may  consider  the  expansion  in  length,  or  linear  expansion, 
only ;  or  the  expansion  in  length  and  breadth,  or  superficial 
expansion ;  or  expansion  in  length,  breadth,  and  thickness, 
or  cubical  expansion.  Though  we  may  consider  these  ex- 
pansions apart,  they  in  reality  all  occur  together. 

Fig. 


The  linear  expansion  of  a  solid  may  be  illustrated  by 
means  of  the  apparatus  shown  in  Figure  151.  The  metal 
rod  A  is  supported  on  two  standards.  It  is  fastened  at 
the  end  B  by  the  binding  screw.  The  other  end  passes 
loosely  through  its  standard,  and  presses  against  the  short 


158  NATURAL    PHILOSOPHY. 

arm  of  the  index  K,  which  moves  over  a  graduated  arc. 
Under  the  rod  there  is  a  vessel  filled  with  alcohol.  The 
rod  is  adjusted  so  that  the  index  shall  be  at  zero  on  the 
scale,  and  the  alcohol  is  lighted.  As  the  alcohol  burns, 
the  rod  becomes  heated,  and  the  index  rises.  The  rise  of 
the  index  shows  that  the  rod  has  expanded  in  length  so  as 
to  move  forward  the  short  arm  of  the  index. 

If  a  brass  and  iron  rod  of  the  same  length  and  thick- 
ness are  tried  in  succession,  and  each  is  raised  to  a  bright 
red  heat,  it  will  be  found  that  the  brass  rod  will  expand 
considerably  more  than  the  iron.  As  a  rule  different  solids 
expand  unequally  when  heated  equally. 

Fig.    !52. 


The  cubical  expansion  of  a  solid  may  be  illustrated  by 
means  of  the  ring  and  ball  shown  in  Figure  152.  When 
cool,  the  ball  will  just  pass  through  the  ring.  If  we  heat 
the  ball  by  holding  it  for  a  time  in  the  flame  of  the  lamp, 
it  will  no  longer  pass  through  the  ring  ;  but  if  allowed  to 
cool,  it  will  again  pass  through  the  ring.  If,  while  the 
heated  ball  rests  on  the  ring,  the  ring  is  heated  equally 
with  the  ball,  the  latter  will  again  pass  through  the  ring, 
the  two  being  equally  expanded  by  the  heat. 

194.  Force  of  Expansion  of  Solids.  —  The  force  of  ex- 
pansion is  very  great,  being  equal  to  that  which  would  be 
necessary  to  compress  the  body  to  its  original  dimensions. 
Thus,  for  instance,  iron  when  heated  from  32°  to  212° 


NATURAL    PHILOSOPHY. 


'59 


Fig.  153. 


increases  by  .0012  of  its  original  length.  In  order  to  pro- 
duce a  corresponding  change  of  length  in  a  rod  an  inch 
square,  a  force  of  about  15  tons  would  be  required.  It 
would  be  useless  to  attempt  to  offer  any  mechanical  resist- 
ance to  a  force  so  enormous ;  the  only  thing  that  can  be 
done,  in  the  case  of  structures  in  which  metals  are  em- 
ployed, is  to  arrange  the  parts  in  such. a  manner  that  the 
expansion  shall  not  be  attended  with  any  evil  effects. 
Thus,  in  a  railway,  the  rails  do  not  touch  each  other,  a 
small  interval  being  left  to  allow  room  for  the  variations  of 
length.  Iron  beams  employed  in  buildings  must  have  the 
ends  free  to  move  forward,  without  encountering  any  ob- 
stacles, which  they  would  inevitably  overthrow.  Sheets  of 
zinc  and  lead  employed  in  roofing  are  so  arranged  as  to  be 
able  to  overlap  one  another  on  expansion. 

195.  Compensating  Pendulum.  — vThe  pen- 
dulum, as  we  know,  regulates  the  motion  of  a 
clock.  Suppose  the  clock  to  keep  exact  time 
at  the  temperature  of  the  freezing-point ;  then, 
if  the  temperature  rises,  the  length  of  the  pen- 
dulum will  increase,  and  with  it  the  duration 
of  each  oscillation,  so  that  the  clock  will 
lose.  The  opposite  effect  would 
be  produced  by  a  fall  of  the 
temperature  below  the  freezing- 
point.  We  thus  see  that  clocks 
are  liable  to  go  too  fast  in 
winter,  and  too  slow  in  sum- 
mer, and  that  we  must  move  * 
the  ball  of  the  pendulum  from 
time  to  time  in  order  to  insure 
their  regularity. 

The  effect  of  temperature  may 
be  notably  diminished  by  means 
of  compensating  pendulums,  of 
which  there  are  several  different 
kinds. 


Fig.  154. 


i6o 


NATURAL   PHILOSOPHY. 


Fig.  .55 


Harrison's  gridiron  pendulutn  (Figures  153  and  154)  con- 
sists of  four  oblong  frames,  the  uprights  of  which  are  alternately 
of  brass,  C,  and  of  steel,  F.  The  brass  uprights  rest  upon  the 
bottom  cross-bars  of  the  steel  frames.  The  second  pair  of 
steel  uprights  are  suspended  from  the  cross-bar  resting  on  the 
top  of  the  first  pair  of  brass  uprights.  The  pendulum  rod  is 
hung  from  the  top  cross-bar  of  the  second  pair  of  brass  uprights. 
It  will  be  seen  that  the  expansion  of  the  steel  rods  alone  would 
tend  to  lower  the  ball,  while  the  expansion  of  the  brass  rods  alone 
would  tend  to  raise  it.  The  lengths  of  the  steel  rods  are,  of 
course,  greater  than  those  of  the  brass  rods ;  but  as  brass  ex- 
pands more  rapidly  than  steel,  the  lengths  of  the  rods  may  be  so 
adjusted  that  the  expansion  of  one  set  of  rods  shall  just  balance 
that  of  the  other,  so  that  the  ball  of  the  pendulum  shall  be  kept 
all  the  time  at  exactly  the  same  distance  from  the  point  of  sus- 
pension. 

Graham's  pendulum  consists  of  an  iron  rod 
carrying  at  the  bottom  a  frame  which  holds 
one  or  two  tubes  containing  mercury  (Figure 
155).  The  mercury  takes  the  place  of  the  ball 
of  the  pendulum.  The  expansion  of  the  rod 
alone  would  tend  to  lower  the  centre  of  gravity 
of  the  mercury,  while  the  expansion  of  the  mer- 
cury alone,  since  the  mercury  is  free  to  expand 
only  upward,  would  tend  to  raise  the  centre  of 
gravity.  The  quantity  of  mercury  is  adjusted 
so  that  its  expansion  shall  balance  that  of  the 
rod,  and  thus  keep  the  centre  of  gravity  of 
the  mercury  at  the  same  height  all  the  time. 

196.  Compensation  Balance- Wheel.  —  The 
rate  of  a  watch  is  con-  Fig.  156. 

trolled  by  the  vibration 
of  the  balance-wheel. 
The  larger  this  wheel, 
the  slower  it  vibrates, 
and  the  smaller  it,  is 
the  faster  it  vibrates. 
Hence  changes  of  tem- 
perature have  the  same 


NATURAL   PHILOSOPHY. 


161 


Fig.  157- 


effect  on  the  rate  of  watches  as  on  that  of  clocks.  The  rim  of  the 
compensation  balance-wheel'^  made  in  sections,  which  are  sup- 
ported by  metallic  rods,  radiating  from  the  centre  of  the  wheel 
(Figure  156).  The  sections  are  weighted  at  their  free  ends,  and 
are  composed  of  two  metals  having  different  degrees  of  expansi- 
bility, the  more  expansible  metal  being  on  the  outer  side  of  the 
sections.  The  expansion  of  the  rods  alone  would  tend  to  carry 
the  weights  away  from  the  centre  of  the  wheel  and  so  to  make 
the  wheel  larger.  When  the  sections  of  the  rim  expand,  they 
become  more  curved,  since  they  expand  more  rapidly  on  the 
outside  than  on  the  inside.  Hence  the  expansions  of  the  sec- 
tions alone  would  tend  to  carry  the  weight  in  towards  the  centre 
and  so  to  make  the  wheel  smaller.  The  parts  of  the  wheel  may 
be  so  adjusted  that  the  expansion  of  the  sections  of  the  rim 
shall  just  balance  that  of  the  supporting  rods. 

197.  Expansion  of  Liquids.  —  The  expansion  of  a  liquid 
may  be  illustrated  by  means  of  a  bulb  with  a  projecting 
tube,  as  shown  in  Figure  157. 
The  bulb  and  stems  are  filled 
with  water  or  other  liquid  up  to 
the  point  a.  On  immersing  the 
bulb  into  a  vessel  of  hot  water, 
the  liquid  in  the  stem  at  first 
falls  to  b,  and  then  gradually  rises 
to  a.  The  liquid  falls  at  first, 
because  the  bulb,  being  the  first 
heated,  is  also  the  first  to  expand, 
and  as  the  capacity  of  the  bulb 
increases,  the  liquid  falls  in  the 
stem.  Afterwards,  as  the  liquid 
becomes  heated,  it  also  expands, 
and  that  more  rapidly  than  the 
globe.  Hence  the  rise  of  the 
liquid  in  the  tube. 

If   two   bulbs,  with    projecting    ^j 
tubes,  and   of   exactly  the   same 


1 62  NATURAL    PHILOSOPHY. 

size,  are  filled,  one  with  water  and  the  other  with  alcohol, 
and  are  th&n  heated  equally,  the  alcohol  will  be  seen  to 
expand  more  rapidly  than  the  water.  And  in  general, 
different  liquids  when  heated  equally  expand  unequally. 

198.  Anomalous  Expansion  and  Contraction  of  Water. — 
If  a  bulb  and  tube  are  filled  with  water,  and  the  bulb  sur- 
rounded with  a  freezing  mixture,  the  water  in  the  stem  will 
steadily  fall  till  the  temperature  of  the  water  has  reached 
39°  ;  it  will  then  begin  to  rise  again,  and  will  continue  to 
rise  till  the  temperature  reaches  32°.  If  now  the  bulb  is 
gradually  heated,  the  water  will  fall  in  the  stem  till  the 
temperature  reaches  39° ;  it  will  then  begin  to  expand, 
and  will  continue  to  expand  until  it  boils.  Water  at  39° 
will  expand  whether  it  is  heated  or  cooled.  It  follows 
from  this,  that  water  is  at  its  greatest  density  at  39°. 
Hence  this  point  of. temperature  is  called  its  point  of  maxi- 
Fig.  158.  mum  density. 

199.  Expansion  of  Gases.  —  The  ex- 
pansion of  air  may  be  illustrated  by  means 
of  the  bulb  and  tube  shown  in  Figure 
158.     The  bulb  is  filled  with  air,  which 
is  separated  from  the  external  air  by  a 
small    column   of    liquid    in    the    stem, 

,  which  serves  also  as  an  index.  When 
the  globe  is  warmed  by  the  hands,  the 
index  is  rapidly  pushed  up,  showing 
that  the  air  has  expanded.  It  has  been 
found  that  all  gases  expand  equally  for 
the  same  rise  of  temperature,  and  that 
under  a  uniform  pressure  a  gas  will 
expand  so  as  to  double  its  volume  for  a 
rise  of  temperature  of  about  490°. 

200.  Expansion  due  to  an  Increase  of 
\folecnlar  Motion.  —  The  molecules  of  bodies  are  all  the  time 
moving  rapidly  to  and  fro.     When  heat  is  applied  to  a  body, 


NATURAL    PHILOSOPHY. 


its  molecules  are  made  to  move  more  rapidly,  and  this  increased 
agitation  of  the  molecules  causes  them  to  move  farther  apart, 
and  the  body  to  expand. 

B.   MEASUREMENT  OF  TEMPERATURE. 

201.  Temperature.  —  When  we  wish  to  indicate  how  hot 
a  body  is,  we  say  that  it  has  a  certain  temperature.     The 
word  temperature  is  the   noun  which   corresponds  to  the 
adjective  hot.     We  estimate  how  hot  a  body  is  from  its 
power  of  imparting  heat  to  other  bodies.     The  body  which 
has  the  greater  power  of  imparting  heat  is  said  to  be  the 
hotter,  or  to  have  the  higher  temperature. 

Temperature  is  the  thermal  condition  of  a  body  considered 
with  reference  to  its  power  of  imparting  heat  to  other  bodies. 

An  instrument  used  for  measuring  temperature  is  called 
a  thermometer. 

202.  Mercurial  Thermometer.  —  In  ordinary  thermome- 
ters changes  of  temperature  are  indicated  and  measured 
by  the  expansion  and  contraction  of  mercury. 

The  instrument  is  called  a  mercurial  ther- 
mometer. It  consists  essentially,  as  shown  in 
Figure  159,  of  a  tube  with  a  very  fine  calibre, 
closed  at  one  end,  and  having  a  reservoir  at 
the  other  end,  usually  in  the  form  of  a  globe 
or  cylinder.  The  bulb  and  a  portion  of  the 
stem  are  filled  with  mercury.  As  the  tem- 
perature changes,  the  top  of  the  column  of 
mercury  in  the  tube  rises  and  falls.  A  scale 
is  either  engraved  on  the  stem  or  placed 
behind  it. 

203.  Construction  of  the  Afercurial  Thermom- 
eter. —  The  construction  of  a  mercurial  thermom- 
eter involves  four  different  operations  :    (i)  The 
choice  of  the  tube;  (2)  The  filling  of  the  tube ; 
(3)  The  determination  of  the  fixed  points  of  tem- 
perature ;  (4)  The  graduation  of  the  thermometer. 


164 


NATURAL    PHILOSOPHY. 


(i.)  The  first  object  is  to  procure  a  tube  of  as  uniform  bore 
as  possible.  In  order  to  ascertain  whether  this  condition  is  ful- 
filled, a  small  column  of  mercury  is  introduced  into  the  tube, 
and  its  length  in  different  parts  of  the  tube  is  measured.  If 
these  lengths  are  exactly  equal,  the  tube  must  be  of  uniform 
bore.  This  is  not  generally  the  case,  and  we  have  to  content 
ourselves  with  an  approximation  to  this  result;  but  we  must 
reject  tubes  in  which  the  differences  of  length  observed  are  too 
great.  When  a  suitable  tube  has  been  obtained,  a  reservoir  is 
either  blown  at  one  end  or  attached  by  melting,  the  former  plan 
being  usually  preferable. 

(2.)    After  the  tube  has  been  chosen  and  the  reservoir  has 
been  formed,  a  little  cup  is  formed  at  the  open  end  of  the  stem 
either  of  glass  or  of  paper.     This  cup  is  partly  filled  with  mer- 
Fig  160  cury  (Figure  160).     The  stem  is  then  held  in 

a  slightly  inclined  position,  and  the  bulb  is 
gently  heated.  The  heat  expands  the  air  in 
the  bulb,  and  drives  out  a  part  of  it  through 
the  mercury  in  the  cup.  The  bulb  is  now 
allowed  to  cool,  the  air  in  it  contracts,  and 
some  of  the  mercury  in  the  cup  falls  into  the 
bulb  to  take  the  place  of  the  air  which  has 
been  expelled.  The  bulb  is  again  heated  so 
as  to  boil  the  mercury  in  it  for  a  short  time. 
As  the  mercury  boils,  its  vapor  drives  the  air 
completely  out  of  the  bulb  and  stem.  The 
bulb  is  again  allowed  to  cool,  the  vapor  of 
mercury  in  the'  bulb  and  stem  condenses,  and 
the  mercury  from  the  cup  passes  into  the  bulb 
and  stem  so  as  completely  to  fill  both.  The 
bulb  is  now  heated  to  a  temperature  a  little 
above  the  highest  temperature  the  thermome- 
ter is  designed  to  measure,  and  while  the  bulb  is  still  heated, 
the  upper  end  of  the  stem  is  melted  off,  by  means  of  a  blow- 
pipe, so  as  to  close  the  stem  air-tight.  The  thermometer  is 
thus  sealed.  When  the  bulb  is  allowed  to  cool  again,  the 
mercury  in  the  stem  falls,  leaving  a  vacuum  above  it. 


(3.)    The  two  fixed  points  of  temperature  are  those  at 


NATURAL    PHILOSOPHY.  165 

which  ice  melts  and  water  boils.     The  former  is  called  the 
freezing-point,  and  the  latter  the  boiling-point. 

Under  the  same  pressure  it  has  been  found  that  ice  always 
melts  at  the  same  temperature,  while  the  temperature  at  which 
water  freezes  varies  somewhat  with  the  conditions  under  which 
the  experiment  is  tried.  In  order  to  determine  the  position  of 
the  freezing-point  on  the  stem,  the  bulb  and  the  lower  part 
of  the  stem  are  surrounded  by  melting  ice,  contained  in  a  per- 
forated vessel  so  as  to  allow  the  water  Fjg.  ,6l. 
produced  by  the  melting  to  escape  f 
(Figure  161).  When  the  column  in 
the  stem  ceases  to  fall,  a  mark  is  made 
on  the  tube,  with  a  fine  diamond,  at 
the  top  of  the  mercurial  column.  This 
mark  indicates  the  position  of  the 
freezing-point  for  this  particular  ther- 
mometer. 

When  water  is  boiling  under  the 
average  atmospheric  pressure,  the  tem- 
perature of  the  steam  just  over  the 
water  is  found  to  be  uniform,  while 
that  of  the  water  varies  somewhat  with  other  circumstances  than 
the  pressure.  In  order  to  obtain  the  position  of  the  boiling- 
point,  the  bulb  and  stem  of  the  thermometer  are  enveloped  in 
steam  from  boiling  water,  as  shown  in  Figure  162.  The  height 
to  which  the  mercury  rises  is  then  marked  on  the  stem. 

(4.)  There  are  two  thermometer  scales  in  common  use, 
namely,  the  Fahrenheit  and  the  Centigrade.  The  ordinary 
scale  in  use  in  this  country  and  in  England  is  the  Fahren- 
heit scale.  On  this  scale  the  freezing-point  is  marked  32 
and  the  boiling-point  212.  The  space  between  the  freez- 
ing and  boiling-points  is  divided  into  180  equal  parts,  each 
of  which  is  called  a  degree.  These  divisions  are  continued 
on  the  scale  above  the  boiling-point  and  below  the  freezing- 
point  to  the  ends  of  the  tube.  A  Fahrenheit  degree  is 
T^JJ  of  the  difference  of  temperature  between  the  freezing 
and  boiling  points. 


1 66 


NATURAL   PHILOSOPHY. 


On  the  Centigrade  scale  the  freezing-point  is  marked  o 
and  the  boiling-point  100,  and  the  space  between  the  two 
is  divided  into  100  equal  parts,  the  divisions  being  con- 
tinued to  the  ends  of  the  tube.  A  Centigrade  degree  is 
Tg^j  of  the  difference  of  temperature  between  the  freez- 
ing and  boiling  points.  A  Fahrenheit  degree  is  $  of  a 
Centigrade  degree. 


The  zero  of  the  Centigrade  scale  is  the  temperature  of 
melting  ice.  The  zero  of  the  Fahrenheit  scale  is  32°  F. 
below  the  melting-point  of  ice.  It  was  the  lowest  tempera- 
ture that  Fahrenheit  could  obtain  with  a  mixture  of  salt 
and  ice. 

204.   Alcohol  Thermometers.  —  Mercury  freezes  at  a  tem- 


NATURAL   PHILOSOPHY. 


i67 


perature  of  about  40°  below  zero,  or  of  —  40°  F.  Hence 
mercury  cannot  be  used  for  measuring  temperatures  below 
that  point.  Low  temperatures  are  sometimes  measured  by 
means  of  an  alcohol  thermometer.  An  alcohol  thermom- 
eter is  constructed  in  the  same  way  as  a  mercurial  ther- 
mometer, but  the  bulb  is  rilled  with  alcohol  instead  of 
mercury.  As  alcohol  boils  at  a  temperature  of  about 
175°  F.,  an  alcohol  thermometer  cannot  be  used  for  meas- 
uring high  temperatures. 

205.  Pyrometers.  —  Mercury  boils  at  a  temperature  of 
about  670°  F.  Hence  a  mercurial  thermometer  cannot  be 
employed  to  measure  temperatures  above  that  point.  Very 
high  temperatures  are  often  measured  by  the  expansion  of 
solids.  The  instrument  used  is  called  a  pyrometer.  One 
form  of  a  pyrometer  is  shown  in  Figure  163.  It  consists 

Fig.  163.  Fig.  .64. 


of  a  bar  of  iron  lying  in  the  groove  of  a  por- 
celain slab.  One  end  of  the  iron  bar  presses 
against  the  end  of  the  groove,  and  the  other 
end  against  the  arm  of  an  indicator.  As  the 
bar  expands  it  moves  the  index,  point,  the 
position  of  which  indicates  roughly  the  tem- 
perature to  which  the  bar  is  exposed.  Such 
pyrometers  are  not  found  to  be  very  accurate. 

206.  Air  Thermometer.  —  The  air  thermometer,  though 
somewhat  troublesome  to  manage,  is  the  most  accurate  of  all 
thermometers.  One  form  of  this  instrument  is  shown  in  Figure 
164.  The  reservoir  A  of  glass  or  porcelain  is  filled  with  air. 
and  connects,  by  means  of  a  narrow  tube,  with  the  upright  tube 
B  C,  which  is  partially  filled  with  mercury.  The  tube  Z?Ccon- 


1 68  NATURAL    PHILOSOPHY. 

nects  with  a  second  tube  DE  open  at  the  top  and  filled  with 
mercury  to  the  height  of  the  mercury  in  B  C,  that  the  air  in  the 
reservoir  may  be  subjected  to  the  pressure  of  the  atmosphere. 
The  tube  B  C  is  graduated.  When  the  reservoir^  is  heated, 
the  air  in  it  expands  and  drives  the  mercury  down  in  the  tube 
B  C.  By  means  of  the  stop-cock  at  the  bottom,  the  mercury 
is  kept  at  the  same  height  in  both  tubes,  that  the  pressure 
on  the  enclosed  air  may  be  always  the  same. 

The  globe  A  is  made  of  glass  unless  the  temperatures  to  be 
measured  are  above  the  melting-point  of  this  substance,  in 
which  case  the  globe  is  of  porcelain. 

207.  Absolute  Zero.  —  If  the  air  thermometer  is  constructed 
of  a  simple  tube  of  uniform  size  throughout,  without  any  en- 
largement at  the  end,  and  this  tube  is  graduated  in  the  same 
way  as  an  ordinary  mercurial  thermometer,  by  first  marking  the 
freezing  and  boiling  points  on  it,  and  then  dividing  the  space 
between  them  into  180  equal  parts,  and  continuing  the  divisions 
down  to  the  closed  end  of  the  tube,  it  will  be  found  that  the  last  di- 
vision will  indicate  —  459°  F.  This  temperature  is  called  abso- 
lute zero,  and  temperature  measured  from  this  point  is  called 
F-  l6  absolute  temperature  (119)- 

208.  Differential  Thermometer. 
—  Leslie  of  Edinburgh  invented, 
in  the  beginning  of  the  present 
century,  an  ingenious  instrument 
which  enables  us  to  measure 
small  variations  of  temperature. 
A  column  of  sulphuric  acid, 
colored  red,  stands  in  the  two 
branches  of  a  bent  tube,  the  ex- 
tremities of  which  terminate  in 
two  globes  of  equal  volume  (Fig- 
ure 165).  When  the  air  con- 
tained in  the  two  globes  is  at  the 
same  temperature,  whatever  that 
temperature  may  be,  the  liquid, 
if  the  instrument  is  in  order,  stands  at  the  same  height 


NATURAL   PHILOSOPHY.  169 

in  the  two  branches.  This  point  is  marked  zero.  One  of 
the  globes  being  then  maintained  at  a  constant  tempera- 
ture, the  other  is  raised  through,  for  instance,  5  degrees, 
when  the  column  rises  on  the  side  of  the  colder  globe  up  to 
a  point  a,  and  descends  on  the  other  side  to  a  point  b.  Sup- 
pose the  space  traversed  by  the  liquid  in  each  branch  to 
be  divided  into  10  equal  parts,  each  part  will  be  equivalent 
to  a  quarter  of  a  degree.  This  division  is  continued  upon 
each  branch  on  both  sides  of  zero. 

This  differential  thermometer,  as  it  is  called,  is  an  instrument 
of  great  sensibility,  and  enabled  Leslie  to  make  some  very 
delicate  investigations  on  the  subject  of  the  radiation  of  heat. 
It  is  now,  however,  superseded  by  the  thermopile  invented 
by  Melloni,  and  the  thermal  balance  invented  by  Professor 
Langley.  These  instruments  will  both  be  described  under 
the  head  of  electricity. 

C.   CHANGE  OF   STATE. 

/.  FUSION  AND  SOLIDIFICATION. 

209.  Fusing-Point.  —  When  any  solid  is  sufficiently 
heated  it  will  melt,  but  different  solids  melt  at  very  differ- 
ent temperatures.  The  temperature  at  which  any  solid 
melts  is  called  its  melting-point  or  fusing-point.  Mercury 
melts  at  —  40°  F.,  ice  at  32°  F.,  lead  at  608°  F.,  and  silv'er 
at  1832°  F. 

Most  substances  expand  on  melting,  but  a  few,  like  ice, 
contract.  When  a  substance  expands  on  melting,  an  in- 
crease of  pressure  upon  it  will  tend  to  hinder  its  melting, 
and  will  therefore  raise  its  melting-point.  When,  on  the 
other  hand,  the  substance  contracts  on  melting,  an  increase 
of  pressure  will  tend  to  help  its  melting,  and  will  accord- 
ingly lower  its  melting-point. 

The  passage  from  the  solid  to  the  liquid  state  is  gener- 
ally abrupt ;  but  this  is  not  always  the  case.  Glass,  for 
instance,  before  reaching  a  state  of  perfect  liquefaction, 


1JO  NATURAL   PHILOSOPHY. 

passes  through  a  series  of  intermediate  stages  in  which  it  is 
of  a  viscous  consistency,  and  can  be  easily  drawn  out  into 
exceedingly  fine  threads,  or  moulded  into  different  shapes. 

2 1  o.  Constant  Temperature  during  Fusion.  —  During  the 
entire  time  of  fusion  the  temperature  remains  constant. 
Thus,  if  a  vessel  containing  ice  is  placed  on  the  fire,  the 
ice  will  melt  more  quickly  as  the  fire  is  hotter ;  but  if  the 
mixture  of  ice  and  water  is  constantly  stirred,  a  thermom- 
eter placed  in  it  will  indicate  the  temperature  32°  without 
variation,  so  long  as  any  ice  remains  unmelted  ;  it  is  only 
after  all  the  ice  has  become  liquid  that  a  rise  of  tempera- 
ture will  be  observed. 

In  the  same  way,  if  sulphur  is  heated  in  a  glass  vessel,  the 
temperature  indicated  by  a  thermometer  placed  in  the  vessel 
will  rise  gradually  until  it  reaches  about  230°,  when  a  por- 
tion of  the  sulphur  will  melt ;  and  if  the  vessel  is  shaken 
during  the  time  of  fusion,  until  the  whole  of  the  sulphur  is 
liquefied,  the  temperature  will  remain  steadily  at  this  point. 

211.  Latent  Heat  of  Fusion.  —  As  we  have  just  seen,  all 
the  heat  that  enters  a  body  while  it  is  undergoing  fusion  is 
employed  in  changing  its  state.     The  heat  thus  employed 
is  said  to  be  rendered  latent,  and  is  called  the  latent  heat 
of  fusion,  or,  since  it  exists  in  the  latent  state  in  the  liquid 
formed,  the  latent  heat  of  the  liquid. 

212.  Solidification.  —  Were    any    substance    sufficiently 
cooled,  it  would  become  solid.     This  conversion  of  a  sub- 
stance into  a  solid  by  a  reduction  of  temperature  is  called 
solidification,  or  congelation. 

It  has  been  found  that  liquids  can  be  cooled  below  the  melt- 
ing-point of  their  solids  without  congelation.  Liquids  thus 
cooled  below  their  so-called  freezing-points  have,  however,  so  to 
speak,  a  tendency  to  freeze  which  is  kept  in  check  only  by  the 
difficulty  of  making  a  beginning.  If  freezing  once  begins,  or 
if  ever  so  small  a  piece  of  the  same  substance  in  the  frozen 
state  is  allowed  to  come  in  contact  with  the  liquid,  congelation 


NATURAL   PHILOSOPHY.  171 

will  quickly  extend  until  there  is  none  of  the  liquid  left  at  a 
temperature  below  that  of  fusion.  The  condition  of  a  liquid 
cooled  below  its  freezing-point  has  been  aptly  compared  to  that 
of  a  row  of  bricks  set  on  end  in  such  a  manner  that  if  the  first 
is  overturned,  it  will  cause  all  the  rest  to  fall,  each  one  over- 
turning its  successor. 

The  contact  of  its  own  solid  infallibly  produces  congelation 
in  a  liquid  in  this  condition,  and  the  same  effect  may  often  be 
produced  by  the  contact  of  some  other  solid,  especially  of  a 
crystal,  or  by  giving  a  slight  jar  to  the  containing  vessel.  In 
congelation,  an  amount  of  heat  is  always  set  free  just  equal  to 
that  rendered  latent  in  the  melting  of  the  solid  formed. 

Fig.  1 66. 


213.  Change  of  Volume  in  Congelation.  —  In  passing  from 
the  liquid  to  the  solid  state,  bodies  generally  undergo  a 
diminution  of  volume ;  there  are,  however,  exceptions, 
such  as  ice,  bismuth,  silver,  cast-iron,  and  type-metal.  It 
is  this  property  which  renders  these  latter  substances  so 
well  adapted  for  the  purposes  of  casting,  as  it  enables  the 
metal  to  penetrate  completely  into  every  part  of  the  mould. 
The  expansion  of  ice  is  considerable,  amounting  to  about 
*fa  of  its  bulk  ;  its  production  is  attended  with  enormous 
mechanical  force,  just  as  in  the  analogous  case  of  expan- 
sion by  heat. 

Its  effect  in  bursting  water-pipes  is  well  known.  The 
following  striking  experiment  was  performed  by  Major 


172  NATURAL   PHILOSOPHY. 

Williams  at  Quebec.  He  filled  a  1 2-inch  shell  with  water, 
and  closed  it  with  a  wooden  plug,  driven  in  with  a  mallet. 
The  shell  was  then  exposed  to  the  air,  the  temperature 
being  —  18°  F.  The  water  froze,  and  the  plug  was  pro- 
jected to  a  distance  of  more  than  100  yards,  while  a  cylin- 
der of  ice  of  about  8  inches  in  length  was  protruded  from 
the  hole.  In  another  experiment  the  shell  split  in  halves, 
and  a  sheet  of  ice  issued  from  the  rent  (Figure  166). 

It  is  the  expansion  and  consequent  lightness  of  ice 
which  enables  it  to  float  on  the  surface  of  the  water,  and 
to  protect  animal  life  beneath. 

//.  EVAPORATION  AND   CONDENSATION. 

214.  Evaporation  of  Liquids,  —  The  majority  of  liquids, 
when  left  to  themselves  in  contact  with  the  atmosphere, 
gradually  pass  into  the  state  of  vapor  and  disappear.    This 
phenomenon  occurs  much  more  rapidly  with  some  liquids 
than  with  others,  and  those  which  evaporate  most  readily 
are  said  to  be  the  most  volatile.     Thus,  if  a  drop  of  ether 
is  let  fall  upon  any  substance,  it  disappears  almost  instan- 
taneously; alcohol  also  evaporates  very  quickly,  but  water 
requires  a  much  longer  time.     The  change  is  in  all  cases 
accelerated  by  an  increase  of  temperature ;  in  fact,  when 
we  dry  a  body  before  the  fire,  we  are  simply  availing  our- 
selves of  this  property  of  heat  to  hasten  the  evaporation 
of  the  moisture  of  the  body.     Evaporation  may  also  take 
place  from  solids. 

215.  The  Terms  Gas  and  Vapor.  —  The  words  gas  and 
vapor  have  no  essential  difference  of  meaning.     A  vapor 
is  the  gas  into  which  a  liquid  is  changed  by  evaporation. 
Every  gas  is  probably  the  vapor  of  a  certain  liquid.     The 
word  vapor  is  especially  applied  to  the  gaseous  condition 
of  bodies,  which  are  usually  met  with  in  the  liquid  or  solid 
state,  as  water,  sulphur,  etc. ;  while  the  word  gas  generally 
denotes  a  body  which,  under  ordinary  conditions,  is  never 


NATURAL   PHILOSOPHY.  173 

found  in  any  state  but  the  gaseous.  When  the  air  or  any 
other  gas  contains  all  the  vapor  it  can  hold,  it  is  said  to  be 
saturated  with  that  vapor.  The  amount  of  vapor  required 
to  saturate  a  gas  increases  with  the  temperature.  This  may 
be  shown  by  the  following  experiment.  Pour  a  few  drops 
of  water  into  a  glass  flask,  and  then  apply  heat  till  the 
water  is  entirely  evaporated  and  the  flask  appears  dry.  If 
the  flask  is  allowed  to  cool,  moisture  will  collect  on  its 
inner  surface. 

216.  Dry  Air  and  Currents  of  Air  favorable  to  Evapora- 
tion.—  The  dryer  the  air  the  more  rapid  the  evaporation, 
because  the  more  readily  the  atmosphere-will  take  up  the 
vapor  formed.     Currents  of  air  favor  evaporation,  because 
they  prevent  any  layer  of  air  from  remaining  long  enough 
in  contact  with  the  liquid  to  become  saturated  with  vapor. 
Other  things  being  equal,  wet  clothes  will  dry  much  faster 
on  a  windy  day  than  on  a  still  day. 

217.  Latent  Heat  of  Evaporation.  —  Evaporation    is  a 
cooling  process.     If   a  few  drops  of  ether  are  allowed  to 
fall  on  the  hand,  they  will  evaporate  rapidly,  and  a  sensa- 
tion of  cold  will  be  experienced.     If  the  bulb  of  a  ther- 
mometer is  dipped  in  ether  and  removed,  the  ether  which 
adheres  to  it  will  quickly  evaporate,  and  the  mercury  will 
fall  several  degrees.     The  heat  consumed  in  evaporating  a 
liquid  is  called  the  latent  heat  of  evaporation,  or  the  latent 
heat  of  the  vapor. 

218.  Ebullition. — When  a  liquid  contained  in  an  open 
vessel  is  subjected  to  a  continual  increase  of  temperature, 
it  is  gradually  changed  into  vapor,  which  is  dissipated  in 
the  surrounding  atmosphere.     This  action  is  at  first  con- 
fined to  the  surface ;  but  after  a  certain  time  bubbles  of 
vapor  are  formed  in  the  interior  of  the  liquid,  which  rise 
to  the  top,  and  set  the  entire  mass  in  motion  with  more  or 
less  vehemence,  accompanied  by  a  characteristic  noise  ; 
this  is  what  is  meant  by  ebullition,  or  boiling. 


174  NATURAL    PHILOSOPHY. 

If  we  observe  the  gradual  progress  of  this  phenomenon,  — 
for  example,  in  a  glass  vessel  containing  water,  —  we  shall  per- 
ceive that  after  a  certain  time  very  minute  bubbles  are  given  off ; 
these  are  bubbles  of  dissolved  air.  Soon  after,  at  the  bottom  of 
the  vessel,  and  at  those  parts  of  the  sides  which  are  most  directly 
exposed  to  the  action  of  the  fire,  larger  bubbles  of  vapor  are 
formed,  which  decrease  in  volume  as  they  ascend,  and  disappear 
before  reaching  the  surface.  This  stage  is  accompanied  by  a 
peculiar  sound,  indicative  of  approaching  ebullition,  and  the 
liquid  is  said  to  be  singing.  The  sound  is  probably  caused  by 
the  collapsing  of  the  bubbles  as  they  are  condensed  by  the 
colder  water  through  which  they  pass.  Finally,  the  bubbles 
increase  in  number,  growing  larger  as  they  ascend,  until  they 
burst  at  the  surface,  which  is  thus  kept  in  a  state  of  agitation  ; 
the  liquid  is  then  said  to  boil. 

219.  Difference  between  Evaporation  at  the.  Boiling- Point 
and  below  the  Boiling-Point.  —  Below  the  boiling-point 
evaporation  takes  place  only  at  the  surface ;  the  tension,  or 
elastic  force,  of  the  vapor  is  less  than  that  of  the  atmos- 
phere ;  and  only  a  part  of  the  heat  received  by  the  liquid 
is  used  in  converting  the  liquid  into  vapor,  the  temperature 
of  the  liquid  rising  all  the  time  that  heat  is  applied  to  it. 
At  the  boiling-point  evaporation  takes  place  throughout 
the  liquid  ;  the  tension  of  the  vapor  formed  is  equal  to  that 
of  the  atmosphere ;  and  all  the  heat  received  by  the  liquid 
is  used  in  converting  it  into  steam,  the  temperature  remain- 
ing stationary.  The  elastic  force  of  the  vapor  given  off 
by  a  liquid  increases  with  the  temperature,  until  we  reach 
the  boiling-point,  when  it  equals  that  of  the  atmosphere. 
The  boiling-point  of  a  liquid  is  therefore  the  temperature 
at  which  the  elasticity  of  the  vapor  is  equal  to  the  pressure 
of  the  atmosphere  on  the  surface.  It  follows  from  this 
that  the  boiling-point  must  vary  with  the  pressure.  Under 
a  pressure  less  than  that  of  the  atmosphere  the  boiling- 
point  of  water  is  below  212°;  and  under  a  greater  pres- 
sure than  that  of  the  atmosphere  is  above  2? 2°, 


NATURAL    PHILOSOPHY. 


'75 


2  20.   Franklin's  Experiment.  —  Boil  a  little  water  in  a 
flask  long  enough  to  expel  all  the  air  from  the  flask.     Re- 
move the   flask  from   the  Fig.  167. 
source  of  heat  and  cork  it 
securely.     To  render   the 
exclusion   of  the  air   still 
more    certain,    the    flask 
may  be   inverted  with   its 
corked  end   under  water. 
Ebullition    ceases    almost 
instantly.    Pour  cold  water 
over  the  flask  (Figure  167) 
and   the  liquid  will  begin 
to  boil,  and  will  continue 
to   do   so   for  some  time. 
The   contact  of   the   cold 
water  with  the  flask  lowers  the  temperature  and  tension  of 
the  steam  which  presses  on  the  surface  of  the  water,  and 


the  diminution  of  pressure  allows  the 
water  to  boil  at  a  lower  temperature. 

221.  The  Hypsometer. — The  hypsome- 
ter  (Figure  168)  is  an  instrument  used  for 
ascertaining  the  height  of  mountains  by 
means  of  the  boiling-point  of  water.  It 
consists  of  a  little  boiler  heated  by  a  spirit- 
lamp,  and  terminating  in  a  telescopic  tube 
with  an  opening  at  the  side  through  which 
the  steam  escapes.  A  thermometer  dips 
into  the  steam,  and  projects  through  the 
top  of  the  tube  so  as  to  allow  the  tempera- 
ture of  ebullition  to  be  read.  From  the 
boiling-point  as  indicated  by  the  hypsome- 
ter,  the  pressure  of  the  atmosphere  can 
be  ascertained,  and  from  this  the  height  of 
the  mountain,  in  the  same  way  as  with  the 
barometer. 


Fig.  168. 


i76 


NATURAL    PHILOSOPHY. 


222.  PapMs  Digester.  —  In  a  confined  vessel  water  may  be 
raised  to  a  higher  temperature  than  would  be  possible  in  the 
open  air,  but  it  will  not  boil.     This  is  the  case  in  the  apparatus 
invented  by  the  celebrated  Papin,  and  called  after  him  Papiii's 
digester  (Figure  169).     It  is  a  bronze  vessel  of  great  strength, 
covered  with  a  lid  secured  by  a  powerful  screw.     It  is  employed 

Fig.  169.  for  raising  water  to  very  high 

temperatures,  and  thus  obtain- 
ing effects  which  would  not 
be  possible  with  water  at 
212°,  such,  for  example,  as 
dissolving  the  gelatine  con- 
tained in  bones. 

It  is  to  be  observed  that 
the  tension  of  the  steam  in- 
creases rapidly  with  the  tem- 
perature, and  may  finally 
acquire  an  enormous  power. 
Thus,  at  392°,  the  pressure  is 
that  of  16  atmospheres,  or 
about  240  pounds  on  the 
square  inch.  In  order  to  ob- 
viate the  risk  of  explosion,  Papin  introduced  a  device  for  pre- 
venting the  pressure  from  exceeding  a  definite  limit.  This  in- 
vention has  since  been  applied  to  the  boilers  of  steam-engines, 
and  is  well  known  as  the  safety-valve.  It  consists  of  an  open- 
ing, closed  by  a  conical  valve  or  stopper,  which  is  pressed  down 
by  a  lever  loaded  with  a  weight.  Suppose  the  area  of  the  lower 
end  of  the  stopper  to  be  I  square  inch,  and  that  the  pressure  is 
not  to  exceed  10  atmospheres,  corresponding  to  a  temperature 
of  356°.  The  magnitude  and  position  of  the  weight  are  so 
arranged  that  the  pressure  on  the  whole  is  10  times  15  pounds. 
If  the  tension  of  the  steam  exceeds  10  atmospheres,  the  lever 
will  be  raised,  the  steam  will  escape,  and  the  pressure  will  be 
thus  relieved. 

223.  Condensation    of    Vapors.  —  Condensation,    or    the 
conversion   of   a  vapor  into   a  liquid,  is   the   reverse   of 
evaporation.     In  condensation,  the  heat  rendered  latent 


NATURAL    PHILOSOPHY. 


I77 


Fig.  170. 


in  evaporation  is  again  set  free  as  sensible  heat.  As  an 
increase  of  temperature  and  a  diminution  of  pressure 
promote  evaporation,  so  a  diminution  of  temperature  and 
an  increase  of  pressure  promote  condensation. 

224.  Distillation.  —  Distillation  consists  in  boiling  a  liquid 
and   condensing  the  vapor  evolved.     It  enables  us  to  separate  a 
h'quid  from  the  soKd  matter  dissolved  in  it,  and  to  effect  a  par- 
tial separation  of  the  more  volatile  constituents  of  a  mixture 
from  the  less  volatile. 

The  apparatus  employed  for  this  purpose  is  called  a  still. 
One  of  the  simpler  forms,  suitable  for  distilling  water,  is  shown 
in  Figure  170. 

It  consists  of  a  retort 
#,  the  neck  of  which 
c  communicates  with  a 
spiral  tube  d d,  called 
the  worm,  placed  in  the 
vessel  ^,  which  contains 
cold  water.  The  water 
in  the  retort  is  raised 
to  ebullition,  the  steam 
given  off  is  condensed 
in  the  worm,  and  the  dis- 
tilled water  is  collected 
in  the  vessel^. 

As  the  condensation  of  the  steam  proceeds,  the  water  of  the 
cooler  becomes  heated,  and  must  be  renewed.  For  this  purpose 
a  tube  descending  to  the  bottom  of  the  cooler  is  supplied  with 
a  continuous  stream  of  cold  water  from  above,  while  the  super- 
fluous water  flows  out  by  the  tube  /  at  the  upper  part  of  the 
cooler.  In  this  way  the  warm  water,  which  rises  to  the  top,  is 
continually  removed. 

225.  The  Molecular  Theory  of  Evaporation  and  Condensa- 
tion. —  The  following  account  of  the  molecular  theory  of  evapo- 
ration and  condensation  is  taken  from  Maxwell :    "  We  have 
seen  that  in  the  case  of  a  gas  some  of  the  molecules  have  a  much 
greater  velocity  than  others,  so  that  it  is  only  to  the  average 
velocity  of  all  the  molecules  that  we  can  ascribe  a  definite  value. 


178  NATURAL   PHILOSOPHY. 

It  is  probable  that  this  is  also  true  of  the  motions  of  the  mole- 
cules of  a  liquid,  so  that,  though  the  average  velocity  may  be 
much  smaller  than  in  the  vapor  of  that  liquid,  some  of  the 
molecules  in  the  liquid  may  have  velocities  equal  to  or  greater 
than  the  average  velocity  in  the  vapor.  If  any  of  the  molecules 
at  the  surface  of  the  liquid  have  such  velocities,  and  if  they  are 
moving  from  the  liquid,  they  will  escape  from  those  forces 
which  retain  the  other  molecules  as  constituents  of  the  liquid, 
and  will  fly  about  as  vapor  in  the  space  outside  the  liquid.  This 
is  the  molecular  theory  of  evaporation.  At  the  same  time,  a 
molecule  of  the  vapor  striking  the  liquid  may  become  entangled 
among  the  molecules  of  the  liquid,  and  may  thus  become  part 
of  the  liquid.  This  is  the  molecular  explanation  of  condensa- 
tion. The  number  of  molecules  which  pass  from  the  liquid  to 
the  vapor  depends  on  the  temperature  of  the  liquid.  The  num- 
ber of  molecules  which  pass  from  the  vapor  to  the  liquid  de- 
pends upon  the  density  of  the  vapor  as  well  as  its  temperature. 
If  the  temperature  of  the  vapor  is  the  same  as  that  of  the 
liquid,  evaporation  will  take  place  as  long  as  more  molecules  are 
evaporated  than  condensed ;  but  when  the  density  of  the  vapor 
has  increased  to  such  a  value  that  as  many  molecules  are  con- 
densed as  evaporated,  then  the  vapor  has  attained  its  maximum 
density.  It  is  then  said  to  be  saturated,  and  it  is  commonly 
supposed  that  evaporation  ceases.  According  to  the  molecular 
theory,  however,  evaporation  is  still  going  on  as  fast  as  ever  ; 
only,  condensation  is  also  going  on  at  an  equal  rate,  since  the 
proportions  of  liquid  and  of  gas  remain  unchanged." 

Fig.  ,7I.  226.     Spheroidal     State.  — 

This  is  the  name  given  to  a 
peculiar  condition  which  is  as- 
sumed by  liquids  when  exposed 
to  the  action  of  very  hot  metals. 
If  we  take  a  smooth  plate  of 
iron  or  silver,  and  let  fall  a  drop 
of  water  upon  it,  the  drop  will 
evaporate  more  rapidly  as  the 
temperature  of  the  plate  is  in- 
creased up  to  a  certain  point. 
When  the  temperature  of  the 


NATURAL    PHILOSOPHY. 


179 


plate  exceeds  this  limit,  which,  for  water,  appears  to  be  about 
300°,  the  drop  assumes  a  spheroidal  form,  rolls  about  like  a 
ball  or  spins  on  its  axis,  and  frequently  exhibits  a  "beautiful 
rippling,  as  represented  in  Figure  171.  While  in  this  condi- 
tion it  evaporates  much  more  slowly  than  when  the  plate  was 
at  a  lower  temperature.  If  the  plate  is  allowed  to  cool,  a  mo- 
ment arrives  when  the  globule  of  water  flattens  out,  and  boils 
rapidly  away  with  a  hissing  noise. 

If  the  temperature  of  the  liquid  is  measured  by  means  of  a 
thermometer  with  a  very  small  bulb,  it  is  always  found  to  be 
below  the  boiling-point. 

In  the  spheroidal  state  the  liquid  and  the  metal  plate  do  not 
come  into  contact.  This  fact  can  be  proved  by  direct  obser- 
vation. 

Fig.  172. 


The  plate  used  must  be  quite  smooth  and  accurately  levelled. 
When  the  plate  is  heated,  a  little  water  is  poured  upon  it  and 
assumes  the  spheroidal  state.  By  means  of  a  fine  platinum 
wire  which  passes  into  the  globule,  the  liquid  is  kept  at  the 
centre  of  the  metal  plate.  It  is  then  very  easy,  by  placing  a 
light  behind  the  globule,  to  see  distinctly  the  space  between  the 
liquid  and  the  plate  (Figure  172). 

This  separation  is  maintained  by  the  rush  of 
steam  from  the  under  surface  of  the  globule, 
which  is  also  the  cause  of  the  peculiar  movements 
above  described.  In  consequence  of  the  separa- 
tion, heat  can  pass  to  the  globule  only  by  radia- 
tion, and  hence  its  comparatively  low  temperature 
is  accounted  for. 

The  absence  of  contact  between  a  liquid  and 
a  metal  at  high  temperature  may  be  shown  by 


Fig  173- 


l8o  NATURAL    PHILOSOPHY. 

several  experiments.  If,  for  instance,  a  ball  of  platinum  is 
heated  to  bright  redness,  and  plunged  (Figure  173)  into  water, 
the  liquid  is  seen  to  recede  on  all  sides,  leaving  an  envelope 
of  vapor  around  the  ball.  This  latter  remains  red  for  several 
seconds,  and  contact  does  not  take  place  till  its  temperature  has 
fallen  to  about  300°.  Violent  ebullition  then  takes  place. 

D.  MEASUREMENT  OF  HEAT. 

227.  The  Unit  of  Heat.  —  The  temperature  of  a  body 
indicates  its  thermal  condition,  but  not  the  amount  of  heat 
in  it.     The  thermometer  shows  a  pound  of  iron  and  ten 
pounds  of  iron  to  be  of  the  same  temperature,  when,  of 
course,  the  latter  has  ten  times  as  much  heat  in  it  as  the 
former.    In  the  measurement  of  heat  there  is  needed  some 
unit  in  which  amounts  of  heat  can  be  expressed.     The 
English  unit  of  heat  is  the  amount  of  heat  required  to  raise 
one  pound  of  water  at  32°  one  degree  in  temperature. 

228.  Specific  Heat.  —  If  equal  bulks  of  water  and  of  mer- 
cury are  exposed  to  the  same  source  of  heat,  it  will  be 
found  that  the  temperature  of  the  mercury  will  rise  faster 
than  that  of  the  water,  though  the  mercury  is  more  than 
12  times  as  heavy  as  the  water.     It  has  been  found  that 
it  requires  very  different  amounts  of  heat  to  raise  the  same 
weight  of  different  substances  one  degree  in  temperature. 

The  specific  heat  of  a  substance  is  the  amount  of  heat 
required  to  raise  one  pound  of  it  one  degree  in  tempera- 
ture. The  specific  heat  of  water  is  i,  and  it  is  higher  than 
that  of  any  other  substance,  with  the  single  exception  of 
hydrogen. 

229.  A  Body  in  Cooling  \Q  gives  out  just  as  much  Heat 
as  it  takes  to  Heat  it  i°.  —  Boil  a  quarter  of  a  pound  of 
water  in  a  beaker,  and  the  bulb  of  a  thermometer  plunged 
into  it  will  indicate  a  temperature  of  212°.     Remove  the 
beaker  from  the  source  of  heat,  and  pour  the  water  into 
another  beaker  containing  a  quarter  of  a  pound  of  water 


NATURAL    PHILOSOPHY.  l8l 

of  a  temperature  of  70°.  Stir  the  mixture  a  short  time 
with  the  bulb  of  a  delicate  thermometer,  and  the  tempera- 
ture will  be  found  to  be  141°.  The  first  quarter  of  a  pound 
of  water  has  then  lost  71°,  and  the  second  has  gained  71°  ; 
in  other  words,  the  first  in  cooling  i°  has  given  out  just 
heat  enough  to  warm  the  second  i°.  The  same  is  true  of 
all  other  bodies. 

230.  The  Water  Calorimeter.  —  A  calorimeter  is  an  in- 
strument for  measuring  quantities  of  heat.  The  water 
calorimeter  is  a  vessel  containing  water  into  which  a  heated 
substance  may  be  introduced.  As  the  substance  cools  it 
imparts  some  of  its  heat  to  the  water,  and  the  amount  of 
heat  given  up  by  the  substance  may  be  calculated  from 
the  weight  of  the  water  in  the  calorimeter  and  the  number 
of  degrees  the  temperature  is  raised.  The  number  of  units 
of  heat  received  by  the  water  will  be  equal  to  the  product 
of  the  rise  of  temperature  in  degrees  and  the  weight  of  the 
water  in  pounds. 

The  rise  of  temperature  can  be  ascertained  by  noting 
the  temperature  at  the  beginning  and  at  the  end  of  the 
experiment.  Allowance  must  be  made  for  the  heat  which 
escapes  from  the  water  during  the  experiment.  This 
method  of  measuring  heat  is  called  the  method  of  mix- 
ture, 

To  find  the  specific  heat  of  a  substance  by  this  method,  weigh 
the  substance  to  be  tried,  raise  its  temperature  to  a  known 
point,  and  plunge  it  into  the  calorimeter.  Note  the  temperature 
of  the  water  at  the  beginning  and  end  of  the  experiment,  and 
calculate  the  amount  of  heat  given  to  the  water  by  the  substance 
in  cooling.  The  temperature  of  the  water  at  the  end  of  the 
experiment  will  show  how  many  degrees  the  substance  has 
cooled.  Divide  the  number  of  units  of  heat  which  the  sub- 
stance imparts  to  the  water  in  cooling  by  the  number  of  degrees 
the  substance  has  cooled,  and  the  quotient  will  be  the  amount 
of  heat  given  out  by  the  substance  in  cooling  one  degree.  Di- 
vide the  last  amount  by  the  weight  of  the  substance  in  pounds 


182 


NATURAL    PHILOSOPHY. 


or  fractions  of  a  pound,  and  the  quotient  will  be  the  amount  of 
heat  that  would  be  given  out  by  one  pound  of  the  substance  in 
cooling  one  degree.  This  is  the  specific  heat  of  the  substance. 

231.  The  Latent  Heat  of  Water.  —  By  the  latent  heat  of 
water  we  mean  the  amount  of  heat  required  to  melt  a 
pound  of  ice.  It  is  143  units. 

The  latent  heat  of  water  can  be  found  by  a  process  the  re- 
verse of  that  given  above.  The  calorimeter  is  first  filled  with 
water  at  212°.  We  will  suppose  it  to  hold  ten  pounds  of  water. 
A  piece  of  ice,  weighing  say  a  pound,  is  put  into  the  calorimeter. 
The  water  will  impart  heat  to  the  ice,  which  will  quickly  melt. 
The  resulting  temperature  will  be  182^  degrees.  The  ten 
pounds  of  water  have  fallen  29^-  degrees  in  temperature,  and 
imparted  to  the  ice  293T7T  units  of  heat.  This  heat  has  melted 
the  ice,  and  raised  the  temperature  of  the  pound  of  water  formed 
from  32°  to  i82T7T  degrees,  that  is,  150  T7T  degrees.  To  do  the 
latter  requires  150^-  units.  The  amount  of  heat  deducted  from 
293^  units  leaves  143  units  as  the  amount  of  heat  used  in  melt- 
ing the  pound  of  ice.  Hence  the  latent  heat  of  water  is  143 
units. 

Fig.  174 


232.    The  Ice  Calorimeter.  —  Another  method  of  finding 
specific  heat   is   by  melting  ice.     The  substance  is  first 


NATURAL    PHILOSOPHY.  183 

weighed,  then  heated  to  a  certain  temperature,  as  100°, 
and  placed  in  the  vessel  M  (Figure  174).  This  vessel  is 
placed  within  the  vessel  A,  the  space  between  the  two 
being  filled  with  ice.  The  vessel  A  is  placed  in  another, 
B,  from  which  it  is  also  separated  by  ice.  Since  the 
vessel  A  is  surrounded  by  ice,  the  heat  which  melts  the 
ice  within  it  must  come  wholly  from  the  vessel  M.  As 
the  ice  in  A  melts  the  water  runs  off  through  the  pipe  D. 
As  we  know  how  much  heat  is  required  to  melt  one  pound 
of  ice,  we  need  only  know  how  much  ice  is  melted  by  any 
substance  within  the  box  M,  in  order  to  find  how  many 
units  of  heat  it  has  given  up.  Dividing  this  by  the  weight 
of  the  substance  and  by  the  number  of  degrees  it  has 
cooled,  we  get  its  specific  heat. 

Thus,  suppose  ten  pounds  of  iron  heated  to  132°  are  placed 
in  M,  and  allowed  to  cool  100°  ;  and  that  the  iron  is  found  to 
give  out  109  units  of  heat.  Then,  109  -^-10  =  10.9,  which  is  the 
number  of  units  of  heat  which  would  be  given  out  by  one  pound 
cooling  100°;  and  10.9 -f- 100  =  .109,  which  is  the  number  of 
units  one  pound  would  give  out  in  cooling  i°,  or  the  specific 
heat  of  iron. 

233.  The  Latent  Heat  of  Steam.  —  The  latent  heat  of 
steam  may  be  found  by  allowing  a  quantity  of  steam  to 
pass  into  a  water  calorimeter.  The  steam  will  be  con- 
densed, and  the  water  formed  will  be  cooled  to  the  result- 
ing temperature  of  the  water  in  the  calorimeter.  The  heat 
given  out  in  this  condensation  and  cooling  will  raise  the 
temperature  of  the  water  in  the  calorimeter.  The  amount 
of  this  heat  may  be  calculated  as  in  a  previous  case.  We 
can  also  calculate  the  amount  of  heat  that  is  given 
out  in  the  cooling  of  the  water  formed  from  the  steam. 
The  difference  between  these  two  amounts  will  be  the 
amount  of  heat  set  free  in  the  condensation  of  the  steam. 
This,  divided  by  the  weight  of  the  steam,  will  give  the 
latent  heat  of  steam,  which  is  967  units.  The  latent  heat 


184  NATURAL    PHILOSOPHY. 

of  watery  vapor  is  higher  than  that  of  any  other  known 
vapor. 

QUESTIONS  ON   TEMPERATURE   AND  HEAT. 

102.  Oil  of  vitriol  freezes  at  —  30°  F.     This  is  equivalent  to 
what  temperature  on  the  Centigrade  scale  ?    The  absolute  scale  ? 

103.  Lead  melts -at  620°  F.     At  what  temperature  does  lead 
melt  on  the  Centigrade  scale  and  on  the  absoiute  scale  ? 

104.  Iron  melts  at  2800°  F.    What  is  the  equivalent  tempera- 
ture on  the  Centigrade  scale  and  on  the  absolute  scale  ? 

105.  What   temperatures  on   the    Fahrenheit  and    absolute 
scales  correspond  to  50°  C.  ?     To   —  25°  C.  ?     To  380°  C.  ? 

106.  The  specific  heat  of  iron  is  .109.     How  many  units  of 
heat  would  it  take  to  raise  30  pounds  of  iron  75°  F.  ? 

107.  The  specific  heat  of  silver  is  .055.     How  many  units  of 
heat  would  be  given  out  by  j4  of  a  pound  of  silver  in  cooling 
320°  F.  ? 

108.  The  specific  heat  of  mercury  is  .033.     How  much  heat 
would  it  take  to  raise  23  pounds  of  mercury  125°  F.  ? 

109.  How  much  heat  would  it  take  to  melt  a  cubic  yard  of 
ice,  the  specific  gravity  of  ice  being  .96  ? 

1 10.  How  much  heat  would  be  given  out  by  the  condensation 
of  25  pounds  of  steam  at  a  temperature  of  212°  F.  ? 

in.  How  much  heat  would  it  take  to  convert  a  cubic  yard  of 
water  into  steam  at  a  temperature  of  212°  F.  ? 


II. 

RELATIONS   BETWEEN   HEAT   AND    WORK. 

234.  Heat  consumed  in  the  Performance  of  Work.  —  In 
expansion,  liquefaction  of  solids,  and  evaporation,  the 
molecules  are  always  pushed  into  new  positions  against 
some  kind  of  resistance,  either  internal  or  external ;  that 
is  to  say,  work  is  done  upon  the  molecules.  This  work  is 
always  done  at  the  expense  of  heat,  either  of  that  already 
in  the  body  or  of  that  communicated  to  the  body.  Hence, 
whenever  any  of  these  kinds  of  work  are  done  without  the 


NATURAL    PHILOSOPHY.  185 

application  of  heat  to  the  body,  some  of  the  heat  in  the 
body  is  consumed  and  its  temperature  falls  \  and  whenever 
the  work  is  done  by  the  application  of  heat,  the  tempera- 
ture of  the  body  rises  less  than  it  would  with  the  same 
application  of  heat  were  no  work  done. 

235.  Heat  consumed  in  Expansion.  —  If  a  thermometer 
bulb    is   introduced    into   the    receiver    of    an    air-pump 
through  an  opening  at  the  top  of  the  receiver,  into  which 
the  stem  of  the  thermometer  is  fitted  air-tight  by  means  of 
a  rubber  cork,  and  the  pump  is  worked,  as  the  exhaustion 
proceeds  the  air  in  the  receiver  will  expand  more   and 
more,  and  the  mercury  in  the  stem  of  the  thermometer  will 
fall  several  degrees,  indicating  a  reduction  of  temperature. 
The  air  is  always  chilled  when  any  expansion  takes  place 
in  it  without  the  application  of  heat. 

It  takes  6.7  units  of  heat  to  raise  the  temperature  of  a 
cubic  foot  of  air  490°  when  the  air  is  confined  so  that  it 
cannot  expand,  and  9.5  units  to  raise  the  temperature  the 
same  amount  when  the  air  is  free  to  expand.  In  the  latter 
case  the  air  will  expand  enough  to  double  its  volume.  So 
that  2.8  units  of  heat  are  consumed  in  expanding  a  cubic 
foot  of  air  enough  to  double  its  volume.  The  heat  con- 
sumed in  expansion  is  called  the  latent  heat  of  expansion, 
The  conversion  of  sensible  into  latent  heat  is  simply  the 
transformation  of  kinetic  into  potential  energy.  When  the 
air  contracts  again,  the  potential  energy  is  transformed 
again  into  kinetic  energy,  and  the  latent  heat  again 
becomes  sensible. 

236.  Heat  consumed  in  Liquefaction.  —  Place  some  pul- 
verized nitrate  of  ammonia  in  a  small  beaker  glass,  add  an 
equal  bulk  of  water,  and  stir  the  mixture  with  the  bulb  of 
a  thermometer.     The  solid  will  be  rapidly  dissolved,  and 
the  temperature  of  the  mixture  will  quickly  fall  40  or  50 
degrees.     The  mixture  is  chilled  to  such  an  extent  that,  if 
put  upon  a  wet  board,  the  beaker  will  be  quickly  frozen 


i86 


NATURAL    PHILOSOPHY. 


Fig.  175. 


to  it.  In  the  liquefaction  of  a  solid  a  part  of  its  kinetic 
energy  is  transformed  into  potential  energy,  and  sensible 
heat  becomes  latent  heat.  In  the  solidification  of  the 
liquid,  the  potential  energy  is  transformed  back  again  into 
kinetic  energy,  and  the  latent  heat  again  becomes  sensible 
heat. 

In  the  melting  of  a  solid,  all 
the  kinetic  energy  that  enters  the 
body  is  transformed  into  potential 
energy  by  the  conversion  of  the 
solid  into  a  liquid,  and  hence 
there  is  no  rise  of  temperature 
while  the  solid  is  melting. 

237.  Heat  consumed  in  Evapo- 
ration. —  The  consumption  of  heat 
in  evaporation  may  be  illustrated 
by  means  of  the  cryophorus  (Fig- 
ure 175).  It  consists  of  a  bent  tube  with  a  bulb  at  each 
end.  It  is  partly  filled  with  water,  and  hermetically  sealed 
while  the  liquid  is  in  ebullition,  thus  expelling  the  air. 
When  an  experiment  is  to  be  made,  all  the  liquid  is  passed 
into  the  bulb  £,  and  the  bulb  A  is  plunged  into  a  freezing 
mixture,  or  into  pounded  ice.  The  cold  condenses  the 
vapor  in  A,  and  thus  produces  rapid  evaporation  of  the 
water  in  B.  In  a  short  time  needles  of  ice  appear  on 
the  surface  of  the  liquid. 

If  a  little  water  is  poured  into  a  small  test-tube,  which 
is  placed  in  a  wine-glass  of  ether  (Figure  176),  and  a 
current  of  air  is  blown  through  the  ether  by  means  of 
a  pair  of  bellows,  the  rapid  evaporation  of  the  ether  will 
reduce  the  temperature  sufficiently  to  freeze  the  water  in 
the  tube  in  a  short  time. 

In  evaporation  as  in  liquefaction,  the  conversion  of 
sensible  into  latent  heat  is  merely  the  transformation 
of  kinetic  energy  into  potential  energy. 


NATURAL   PHILOSOPHY.  187 

238.  Freezing  Mixture. — The  ordinary  freezing  mixture 
is  a  mixture  of  salt  and  ice.  The  salt  causes  some  of  the 
ice  to  liquefy,  and  this  liquefaction  of  the  ice  consumes  so 
much  heat  that  the  temperature  of  the  mixture  is  reduced 
sufficiently  to  freeze  cream  within  a  can  which  is  sur- 
rounded by  the  mixture. 

Fig.  176. 


A  mixture  of  solidified  carbonic  acid  and  ether,  in  the 
receiver  of  an  air-pump  from  which  the  air  has  been  ex- 
hausted so  as  to  promote  the  evaporation,  evaporates  with 
very  great  rapidity,  and  the  consumption  of  heat  is  so 
great  as  to  reduce  the  temperature  of  the  mixture  to 
-  166°  F. 

A  mixture  of  solidified  nitrous  oxide  and  bisulphide  of 
carbon,  under  similar  circumstances,  evaporates  still  more 
rapidly,  and  reduces  the  temperature  to  — 220°  F. 

239.  Mamtfacture  of  Ice.  —  Ice  is  now  manufactured  on  a 
large  scale  in  Southern  cities,  by  means  of  liquefied  ammonia 
gas.  The  liquefied  gas  is  passed  into  pipes  similar  to  gas- 
pipes,  arid  then  allowed  to  evaporate  by  diminishing  the  pres- 


l88  NATURAL    PHILOSOPHY. 

sure.  The  pipes  are  bent  around  so  as  to  form  rectangular 
coils,  within  which  are  placed  the  cans  of  water  to  be  frozen. 
The  rapid  evaporation  of  the  liquefied  ammonia  within  the 
pipes  reduces  the  temperature  of  the  coils  sufficiently  to  freeze 
the  water  within  the  cans. 

If  the  pipes  run  to  and  fro  horizontally  under  the  surface  of 
water  in  a  large  tank,  a  continuous  sheet  of  ice  may  be  formed  in 
midsummer. 

240.  Solidification  of  Gases.  —  If  any  gas  is  liquefied 
by  the  combined  action  of  cold  and  pressure,  and  then 

Fig.  177- 


allowed  to  escape  into  the  atmosphere  in  a  fine  stream,  so 
as  to  evaporate  freely,  the  temperature  will  be  reduced  to 
such  an  extent  that  a  portion  of  the  vapor  will  be  frozen, 
so  that  the  gas  can  be  obtained  in  a  solid  state. 

In  the  case  of  hydrogen,  and  some  other  gases,  which 
cannot  be  liquefied  by  the  direct  action  of  cold  and  pres- 
sure, if  the  gas  is  reduced  to  the  greatest  possible  degree 
of  density  by  the  combined  action  of  cold  and  pressure, 
and  then  is  allowed  to  expand  by  a  sudden  removal  of  the 
pressure,  the  sudden  expansion  chills  the  gas  sufficiently 


NATURAL    PHILOSOPHY. 


,Sg 


to  freeze  a  portion  of  it.     Hydrogen  frozen  in  this  way  is 
heard  to  rattle  like  hail  when  it  falls  orr  the  table. 

241.  Faraday's  Method  of  Liquefying  Gases.  —  Most  gases 
may  be  liquefied  by  the  combined  action  of  cold  and  pressure. 
Faraday  was  the  first  who  conducted  methodical  experiments 
in  the  liquefaction  of  gases.  The  apparatus  at  first  employed 
by  him  is  shown  in  Figure  177.  It  consists  of  a  very  strong 
bent  glass  tube,  closed  at  both  ends.  One  end  of  this  contains 
the  ingredients  which,  on  the  application  of  heat,  evolve  the  gas 
to  be  tried,  while  the  other  is  immersed  in  a  freezing  mixture. 
The  pressure  produced  by  the  evolution  of  the  gas  in  large 

Fig.  178. 


quantity  in  a  confined  space  combines  with  the  cold  of  the 
freezing  mixture  to  produce  liquefaction  of  the  gas,  and  the 
liquid  accordingly  collects  in  the  cold  end  of  the  tube. 

242.  Thilorier's  Method  of  Liquefying  Carbonic  Acid  Gas. 
—  Thilorier,  about  the  year  1834,  invented  the  apparatus  shown 
in  Figure  178,  which  is  based  on  this  method  of  Faraday,  and 
is  intended  for  liquefying  carbonic  acid  gas.  This  operation 
requires  the  enormous  pressure  of  about  fifty  atmospheres  at 
ordinary  temperatures.  If  a  slight  rise  of  temperature  occurs 
from  the  chemical  action  attending  the  production  of  the  gas, 
a  pressure  of  75  or  80  atmospheres  may  not  improbably  be  re- 


IQO  NATURAL    PHILOSOPHY. 

quired;  hence  great  care  is  necessary  in  testing  the  strength  of 
the  metal  employed  in  the  construction  of  the  apparatus.  This 
was  formerly  made  of  cast-iron,  and  strengthened  by  wrought- 
iron  hoops ;  but  the  construction  has  since  been  changed,  on 
account  of  a  terrible  explosion,  which  cost  the  life  of  one  of  the 
operators.  At  present,  the  vessels  are  formed  of  three  parts : 
the  inner  one  of  lead;  the  next  £,  which  completely  envelops 
this,  of  copper  ;  and,  finally,  the  hoops  ff  of  wrought-iron, 
which  bind  the  whole  together.  The  apparatus  consists  of  two 
distinct  reservoirs.  In  the  generator  C  is  placed  bicarbonate  of 
soda,  and  a  vertical  tube  a,  open  at  the  top,  containing  sul- 
phuric acid.  By  imparting  an  oscillatory  movement  to  the  vessel 
about  the  two  pivots  which  support  it  near  the  middle,  the 
sulphuric  acid  is  gradually  spilt,  and  carbonic  acid  is  evolved, 
which  becomes  liquid  in  the  interior.  The  generator  is  then 
connected  with  the  condenser  C  by  the  tube  /,  and  the  stop- 
cocks R  and  R'  are  opened.  As  soon  as  the  two  vessels  are  in 
communication,  the  liquid  carbonic  acid  passes  into  the  con- 
denser, which  is  at  a  lower  temperature  than  the  generator,  and 
represents  the  cold  branch  of  Faraday's  apparatus.  The  gen- 
erator can  then  be  disconnected  and  recharged,  and  thus  several 
pints  of  liquid  carbonic  acid  may  be  obtained.  In  the  foregoing 
methods  the  pressure  which  produces  liquefaction  is  furnished 
by  the  evolution  of  the  gas  itself. 

243.  The  Critical  Temperature  of  Gases.  —  Dr.  Andrews,  by 
a  series  of  elaborate  experiments  on  carbonic  acid,  with  the  aid 
of  an  apparatus  which  permits  the  pressure  and  temperature  to 
be  altered  independently  of  each  other,  has  shown  that  at  tem- 
peratures above  88°  F.  this  gas  cannot  be  liquefied,  but,  when 
subjected  to  intense  pressure,  becomes  reduced  to  a  condition 
in  which,  though  homogeneous,  it  is  neither  a  liquid  nor  a  gas. 
When  in  this  condition,  lowering  of  temperature  under  constant 
pressure  will  reduce  it  to  a  liquid,  and  diminution  of  pressure 
at  constant  temperature  will  reduce  ,it  to  a  gas  ;  but  in  neither 
case  can  any  breach  of  continuity  be  detected  in  the  transition. 

On  the  other  hand,  at  temperatures  below  88°  F.,  the  sub- 
stance remains  completely  gaseous  until  the  pressure  reaches  a 
certain  limit  depending  on  the  temperature,  and  any  pressure 
exceeding  this  limit  causes  liquefaction  to  begin  and  to  continue 


NATURAL    PHILOSOPHY. 


till  the  whole  of  the  gas  is  liquefied,  the  boundary  between  the 
liquefied  and  unliquefied  portions  being  all  the  while  sharply 
defined. 

The  temperature  of  88°  may  therefore  be  called  the  critical 
temperature  for  carbonic  acid  ;  and  it  is  probable  that  every 
other  substance,  whether  usually  occurring  in  the  liquid  or  gas- 
eous state,  has  in  like  manner  its  own  critical  temperature,  above 
which  it  is  impossible  to  convert  the  gas  into  a  liquid  by  any 
amount  of  pressure. 

When  a  substance  is  a  little  above  its  critical  temperature, 
and  occupies  a  volume  which  would,  at  a  lower  temperature,  be 
compatible  with  partial  liquefaction,  very  great  changes  of  vol- 
ume are  produced  by  very  slight  changes  of  pressure. 

On  the  other  hand,  when  a  substance  is  at  a  temperature  a 
little  below  its  critical  point,  and  is  partially  liquefied,  a  slight 
increase  of  temperature  leads  to  a  gradual  obliteration  of  the 
surface  of  demarcation  between  the  liquid  and  the  gas ;  and 
when  the  whole  has  been  thus  reduced  to  a  homogeneous  fluid, 
it  can  be  made  to  exhibit  an  appearance  of  moving  or  flickering 
striae  throughout  its  entire  mass  by  slightly  lowering  the  tem- 
perature, or  suddenly  diminishing  the  pressure. 

The  apparatu-s  employed  in  these  remarkable  experiments  is 
shown  in  Figure  1 79,  where  cc  are  two 
capillary  glass  tubes  of  great  strength, 
one  of  them  containing  the  carbonic 
acid,  or  other  gas  to  be  experimented 
on,  the  other  containing  air  to  serve 
as  a  manometer.  These  are  con- 
nected with  strong  copper  tubes  dd, 
of  larger  diameter,  containing  water, 
and  communicating  with  each  other 
through  a  b,  the  water  being  sepa- 
rated from  the  gases  by  a  column  of 
mercury  occupying  the  lower  portion 
of  each  capillary  tube.  The  steel 
screws  ss  are  the  instruments  for 
applying  pressure.  By  screwing 
either  of  them  forward  into  the 
water,  the  contents  of  both  tubes 


192 


NATURAL    PHILOSOPHY. 


are  compressed,  and  the  only  use  of  having  two  is  to  give  a 
wider  range  of  compression.  A  rectangular  brass  case  (not 
shown  in  the  figure),  closed  before  and  behind  with  plate-glass, 
surrounds  each  capillary  tube,  and  allows  it  to  be  maintained  at 
any  required  temperature  by  the  flow  of  a  stream  of  water. 

244.  Mechanical  Equivalent  of  Heat.  —  Meyer  found  the 
equivalent  of  a  unit  of  heat  in  foot-pounds,  by  converting  heat 
into  mechanical  energy  through  the  expansion  of  air.  In  the  ex- 
pansion of  air  the  work  done  is  wholly  external,  namely,  that  of 
pushing  aside  the  surrounding  air.  We  have  seen  that  it  takes 
2.8  units  of  heat  to  expand  a  cubic  foot  of  air  to  double  its  vol- 
ume. To  ascertain  the  amount  of  work  done  in  pushing  away 

Fig.  180. 


the  surrounding  air,  Meyer  imagined  his  cubic  foot  of  air  at  the 
bottom  of  a  prismatic  box  whose  section  was  a  foot  square,  so 
that  the  air  could  expand  only  upward.  The  upper  surface  of 
the  cubic  foot  of  air  contains  144  square  inches.  Hence  the 
weight  of  the  column  of  air  pressing  upon  this  surface  is  about 
144  X  15  =  2160  pounds  ;  and  when  the  cubic  foot  of  air  expands 
so  as  to  double  its  volume,  this  weight  must  be  raised  one  foot 
high.  Hence  2.8  units  of  heat  are  equivalent  to  2160  foot- 
pounds of  mechanical  energy,  and  one  unit  of  heat  to  772  foot- 
pounds, nearly.  This  number  of  foot-pounds  is  the  mechanical 
equivalent  of  heat. 

245.    Joule's  Method  of  finding  the  Mechanical  Equivalent 
of  Heat.  —  Joule  ascertained  the  mechanical  equivalent  of  heat 


NATURAL  PHILOSOPHY. 


'93 


by  converting  mechanical  energy  into  heat  by  means  of  friction. 
He  arranged  his  apparatus  so  that  he  could  measure  both  the 
mechanical  energy  employed  and  the  heat  produced. 

He  constructed  an  agitator,  which  is  somewhat  imperfectly 
represented  in  Figure  180,  consisting  of  a  vertical  shaft,  carry- 
ing several  sets  of  paddles  revolving  between  stationary  vanes, 
these  latter  serving  to  prevent  the  liquid  in  the  vessel  from 
being  bodily  whirled  in  the  direction  of  rotation.  The  vessel 


was  filled  with  water,  and  the  agitator  was  made  to  revolve  by 
means  of  a  cord,  wound  round  the  upper  part  of  the  shaft, 
carried  over  a  pulley,  and  attached  to  a  weight,  which  by  its 
descent  drove  the  agitator,  and  furnished  a  measure  of  the  work 
done.  The  pulley  was  mounted  on  friction-wheels,  and  the 
weight  could  be  wound  up  without  moving  the  paddles.  When 
all  corrections  had  been  applied,  it  was  found  that  the  heat  com- 
municated to  the  water  by  the  agitation  amounted  to  one  unit  for 


IQ4  NATURAL   PHILOSOPHY. 

every  772  foot-pounds  of  work  spent  in  producing  it.  This 
result  was  verified  by  various  other  forms  of  experiment,  and 
may  be  assumed  to  be  correct  within  about  one  foot-pound. 

246.  The  Cylinder  of  the  Steam-Engine.  —  The  molecular 
energy  of  heat  can  be  made  to  do  mechanical  work  by  means  of 
the  arrangement  shown  in  Figure  181.     The  steam  derives  its 
expansive  power  from  the  heat,  and  this  expansive  power  is 
made  to  work  a  piston  in  the  cylinder  of  the  steam-engine.    The 
steam  fr«m  the  boiler  passes  through  the  tube  x  into  the  steam- 
box  d.     Two  pipes  run  from  this  box,  one  a  to  the  top  and  the 
other  b  to  the  bottom  of  the  cylinder.     A  sliding-valve  y  is  so 
arranged  as  always  to  close  one  of  the  pipes  to  the  steam-box 
and  open  it  to  the  exit-pipe  O ;  and,  at  the  same  time,  to  open 
the  other  pipe  to  the  steam-box  and  close  it  to  the  exit-pipe. 
In  the  right-hand  figure,  the  lower  pipe  b  is  open,  and  the  steam 
can  pass  in  under  the  piston  and  force  it  up     At  the  same  time 
the  steam  which  has  done  its  work  on  the  other  side  of  the 
piston  passes  out  from  the  cylinder  through  the  pipes  a  and  O. 

The  sliding-valve  is  connected  by  means  of  the  rod  /  with 
the  crank  of  the  engine,  so  that  it  moves  up  and  down  as  the 
piston  moves  down  and  up.  As  soon,  then,  as  the  piston  has 
reached  the  top  of  the  cylinder,  the  sliding-valve  is  brought  into 
the  position  shown  in  the  left-hand  figure.  The  steam  now 
passes  into  the  cylinder  above  the  piston  through  the  pipe  a,  and 
forces  the  piston  down,  and  the  steam  on  the  other  side  which 
has  done  its  work  goes  out  through  b  and  O.  The  sliding-valve 
is  now  again  in  the  position  shown  in  the  right-hand  figure, 
and  the  piston  is  driven  up  again  as  before;  and  thus  it  keeps 
on  moving  up  and  down,  or  in  and  out. 

III. 

DISTRIBUTION   OF    HEAT. 
A.   CONDUCTION. 

247.  Illustration  of  Conduction.  —  If  heat  is  applied  to 
one  end  of  a  bar  of  metal,  it  is  slowly  propagated  through 
the  substance  of  the  bar,  producing  a  rise  of  temperature 


NATURAL    PHILOSOPHY.  195 

which  is  first  perceptible  near  the  heated  end,  and  after- 
wards in  more  remote  portions.  The  transmission  of  heat 
from  molecule  to  molecule  through  the  substance  of  the 
body  is  called  conduction.  If  the  application  of  heat  to 
one  end  of  the  bar  is  continued  for  a  sufficiently  long 
time,  and  with  great  steadiness,  the  different  portions  of 
the  bar  will  at  length  cease  to  rise  in  temperature,  and  will 
retain  steadily  the  temperatures  which  they  have  acquired. 
We  may  thus  distinguish  two  stages  in  the  experiment  : 
ist,  the  variable  stage,  during  which  all  portions  of  the  bar 
are  rising  in  temperature ;  and,  2d,  the  permanent  state, 
which  may  subsist  for  any  length  of  time  without  altera- 
tion. In  the  former,  the  bar  is  gaining  heat ;  that  is,  it  is 
receiving  more  heat  from  the  source  than  it  gives  out  to 
surrounding  bodies.  In  the  latter,  the  receipts  and  ex- 
penditure of  heat  are  equal,  and  are  equal  not  only  for  the 
bar  as  a  whole,  but  for  every  small  portion  of  which  it  is 
composed. 

In  the  permanent  state  no  further  accumulation  of  heat 
takes  place.  All  the  heat  which  reaches  an  internal  parti- 
cle is  transmitted  by  conduction,  and  the  heat  which  reaches 
a  superficial  particle  is  given  off  partly  by  radiation  and 
air-contact,  and  partly  by  conduction  to  colder  neighboring 
particles.  In  the  earlier  stage,  on  the  contrary,  only  a  por- 
tion of  the  heat  received  by  a  particle  is  thus  disposed  of, 
the  remainder  being  accumulated  in  the  particle,  and  serv- 
ing to  raise  its  temperature. 

In  order  to  obtain  results  depending  on  conduction  free 
from  the  complications  arising  from  differences  of  specific 
heat,  we  must,  in  all  cases,  wait  for  the  permanent  state. 
In  the  earlier  stage  great  specific  heat  acts  as  an  obstacle 
to  rapid  transmission,  and  a  body  of  great  specific  heat 
would  be  liable  to  be  mistaken  for  a  body  of  small  con- 
ductivity. 

248.    Difference  of  Conductivity.  —  The  following  experi- 


196  NATURAL   PHILOSOPHY. 

ments  are  often   adduced  in  illustration  of  the  different 
conducting  powers  of  different  solids. 

Two  bars  of  the  same  size,  but  of  different  materials 

Fig.  182. 


(Figure  182),  are  placed  end  to  end,  and  small  wooden  balls 
are  attached  by  wax  to  their  under  surfaces  at  equal  dis- 
tances. The  bars  are  then  heated  at  their  contiguous  ends, 
and,  as  the  heat  extends  along  them,  the  wax  melts,  and  the 
balls  successively  drop  off.  If  the  heating  is  continued  till 
the  permanent  state  arrives,  it  may  generally  be  concluded 
that  the  bar  which  has  lost  most  balls  is  the  best  con- 
ductor. 

The  well-known  experiment  of  Ingenhousz  is  of  the 
same  kind.  The  apparatus  (Figure  183)  consists  of  a 
copper  box  having  in  one  of  its  faces  a  row  of  holes,  in 
which  rods  of  different  materials  can  be  fixed.  The  rods 
having  been  previously  coated  with  wax,  the  box  is  filled 
with  boiling  water,  which  comes  in  contact  with  the  inner 
ends  of  the  rods.  The  wax  gradually  melts  as  the  heat 
F.  jg  travels  along  the  rods  5 

and  if  the  experiment 
is  continued  till  the 
melting  reaches  its 
limit,  those  rods  on 
which  it  has  extended 
furthest  are,  generally 
speaking,  the  best  conductors.  It  is  thus  found  that 
different  metals  are  not  equally  good  conductors  of  heat, 
and  that  the  more  familiar  ones  may  be  arranged  in  the 


NATURAL    PHILOSOPHY. 


'97 


following  order,  beginning  with  the  best  conductors  :  Silver, 
copper,  gold,  brass,  tin,  iron,  lead,  platinum,  bismuth. 

In  both  these  experiments  we  must  beware  of  attempting 
to  measure  conductivity  by  the  quickness  with  which  the 
melting  advances.  This  quickness  may  be  simply  an  indi- 
cation of  small  specific  heat. 

249.  Conducting  Power  of  Metals.  —  Metals,  though  dif- 
fering considerably  one  from  another,  are  as  a  class  greatly 
superior  in  conductivity  to  other  substances,  such  as  wood, 
marble,   brick,   etc.     This   explains  several  familiar  phe- 
nomena.    If  the  hand  is  placed  upon  a  metal  plate  at  the 
temperature  of    io°C.,  or  plunged   into  mercury  at  this 
temperature,  a  very  marked  sensation  of   cold  is  experi- 
enced.    This   sensation   is   less  intense  with  a   block   of 
marble  at  the  same  temperature,  and  still  less  with  a  piece 
of  wood.     The  reason   is   that  the   hand,  which   is   at  a 
higher  temperature  than  the  substance  to  which  it  is  ap- 
plied, gives  up  a  portion  of  its  heat,  which  is  conducted 
away  by  the  substance;  consequently  a  larger  portion  of 
heat  is  parted  with,  and  a  more  marked  sensation  of  cold 
experienced,  in  the  case  of  the  body  of  greater  conducting 
power. 

250.  Conducting  Powers  of  Liquids. 
—  With  the  exception  of  mercury  and 
other  melted  metals,  liquids  are  exceed- 
ingly  bad   conductors  of    heat.     This 
can  be  shown  by  heating  the  upper  part 
of   a  column   of  liquid,  and  observing 
the   variations    of   temperature   below. 
These  will  be  found  to  be  scarcely  per- 
ceptible,  and  to    be  very  slowly  pro- 
duced.   If  the  heat  were  applied  below 
(Figure  184)  we  should  have  the  pro- 
cess called  convection  of  heat ;  the  lower 
layers  of  liquid  would  rise  to  the  sur- 


Fig.  184. 


i98 


NATURAL    PHILOSOPHY. 


face,  and  be  replaced  by  others,  which  would  rise  in  their 
turn,  thus  producing  a  circulation  and  a  general  heating 
of  the  liquid.  On  the  other  hand,  when  heat  is  applied 
above,  the  expanded  layers  remain  in  their  place,  and  the 
rest  of  the  liquid  can  be  heated  only  by  conduction  and 
radiation. 

The  following  experiment  is  an  illustration  of  the  very 
feeble  conducting  power  of  water.    A  piece  of  ice  is  placed 
Fig.  185.  at   the   bottom   of    a  glass 

tube  (Figure  185),  which  is 
then  partly  filled  with  water  ; 
heat  is  applied  to  the  middle 
of  the  tube,  and  the  upper 
portion  of  the  water  is  readily 
raised  to  ebullition,  without 
melting  the  ice  below. 

251.  Conducting  Power  of 
Gases.  —  Of  the  conducting 
power  of  gases  it  is  almost 
impossible  -to  obtain  any- 
direct  proofs,  since  it  is  ex- 
ceedingly difficult  to  prevent 
the  interference  of  convec- 
We  know,  however,  that  they 
are  exceedingly  bad  conductors.  In  fact,  in  all  cases 
when  gases  are  enclosed  in  small  cavities  where  their 
movement  is  difficult,  the  system  thus  formed  is  a  very  bad 
conductor  of  heat.  This  is  the  cause  of  the  feeble  con- 
ducting powers  of  many  kinds  of  cloth,  of  fur,  eider-down, 
felt,  straw,  saw-dust,  etc.  Materials  of  this  kind,  when 
used  as  articles  of  clothing,  are  commonly  said  to  be 
warm,  because  they  hinder  the  heat  of  the  body  from  escap- 
ing. If  a  garment  of  eider-down  or  fur  were  compressed 
so  as  to  expel  the  greater  part  of  the  air,  and  to  reduce 
the  substance  to  a  thin  sheet,  it  would  be  found  to  be  a 


tion  and  direct  radiation. 


NATURAL    PHILOSOPHY.  199 

much  less  warm  covering  than  before,  having  become  a 
better  conductor.  We  thus  see  that  it  is  the  presence  of 
air  which  gives  these  substances  their  feeble  conducting 
power,  and  we  are  accordingly  justified  in  assuming  that 
air  is  a  bad  conductor  of  heat. 

B.   CONVECTION. 

252.  Convection  Currents.  —  Although  liquids  and  gases 
are  very  poor  conductors  of  heat,  they  allow  heat  to  be 
distributed   through   them    readily  by   convection   currents. 
When  heat  is  applied  to  any  portion  of  a  fluid,  the  heated 
portion  expands,  becomes  lighter,  and  rises,  allowing  colder 
portions  to  take  its  place  and  become  heated   in  turn. 
When  any  portion   of  a  fluid  is  maintained   at  a  higher 
temperature    than    the    surrounding    portion,    the    system 
of  currents  shown  by  the  arrows  in  Figure  184  is  always 
formed.     There  will  be  an  upward  current  at  the  centre  of 
the  heated   region,  an  outflow  in  every  direction  above, 
downward  currents  on  every  side,  and  an  inflow  from  every 
direction  below.     It  is  chiefly  by  such  convection  currents 
that  heat  is  distributed  through  liquids  and  gases. 

C.   RADIATION  AND  ABSORPTION. 

253.  Illustrations  of  Radiation.  —  When  two  bodies  at 
different  temperatures  are  brought  opposite  to  each  other, 
an  unequal  exchange  of  heat  takes  place  through  the  in- 
tervening distance  ;  the  temperature  of  the  hotter  body 
falls,  while  that  of  the  colder  rises,  and  after  some  time 
the  temperature  of  both  becomes  the  same.     This  propa- 
gation of  heat  across  an  intervening  space  is  what  is  meant 
by  radiation,  and  the  heat  transmitted  under  these  condi- 
tions is  called  radiant  heat.     Instances  of  heat  communi- 
cated by  radiation  are  the  heat  of  a  fire  received  by  a 
person  sitting  in  front  of  it,  and  the  heat  which  the  earth 
receives  from  the  sun. 


200  NATURAL    PHILOSOPHY. 

254.  Radiations   will  traverse   a    Vacutim.  —  This   last 
instance  shows  us  that  radiation  as  a  means  of  propagating 
heat  is  independent  of  any  ponderable  medium.    But  since 
the  solar  heat  is  accompanied  by  light,  it  might  still  be 
questioned  whether  dark  heat  could  in  the  same  way  be 
propagated  through  a  vacuum. 

This  was  tested  by  Rumford  in  the  following  way.  He 
constructed  a  barometer  (Figure  186),  the  upper  part  of 
Fig.  186.  which  was  expanded  into  a  globe,  and  con- 
tained a  thermometer  hermetically  sealed 
into  a  hole  at  the  top  of  the  globe,  so  that 
the  bulb  of  the  thermometer  was  at  the 
centre  of  the  globe.  The  globe  was  thus  a 
Torricellian  vacuum-chamber.  By  melting 
the  tube  with  a  blow-pipe,  the  globe  was 
separated,  and  was  then  immersed  in  a  ves- 
sel containing  hot  water,  when  the  ther- 
mometer was  immediately  observed  to  rise 
to  a  temperature  higher  than  could  be  due 
to  the  conduction  of  heat  through  the  stem. 
The  heat  had  therefore  been  communicated 
by  direct  radiation  through  the  vacuum 
between  the  sides  of  the  globe  and  the 
bulb  a  of  the  thermometer. 

255.  Radiant  Heat  travels  in  Straight  Lines.  —  In  a  uni- 
form medium  the  radiation  of  heat  takes  place  in  straight 
lines.     If,   for   instance,   between    a   thermometer   and    a 
source    of    heat    there   are    placed   several    screens,  each 
pierced  with  a  hole,  and  if    the  screens  are  so  arranged 
that  a  straight  line  can  be  drawn  through  the  holes  from 
the   source  to  the  thermometer,  the    temperature  of   the 
latter   immediately   rises ;   if   a  different   arrangement    is 
adopted,  the  heat  is  stopped  by  the  screens,  and  the  ther- 
mometer indicates  no  effect. 

The  hefat  which  travels  along  any  one  straight  line  is 


NATURAL    PHILOSOPHY.  2OI 

called  a  ray  of  heat.  Thus,  we  say  that  rays  of  heat  issue 
from  all  points  of  the  surface  of  a  heated  body,  or  that 
such  a  body  emits  rays  of  heat. 

256.  Molecular  Theory  of  Radiation.  —  According  to  the 
molecular  theory,  radiations  originate  in  the  vibrations  of 
the  atoms  within  the  molecule.    Each  kind  of  atoms  seems 
to  have  certain  characteristic  rates  of  vibration,  and  when 
the  molecules  in   their  motions  come  into  collision,  their 
atoms  are  thrown  into  vibration  ;  these  vibrations  are  com- 
municated to  the  surrounding  ether,  and  are  propagated 
through  the  ether  in  minute  waves  and  with  an  enormous 
velocity.     As  the  temperature  of  the  body  rises  the  agita- 
tion of  its  molecules  becomes  more  energetic,  and  the  more 
violent  collisions  of  the  molecules  produce  more  powerful 
vibrations  of  the  atoms.      Hence  the  radiation  becomes 
more  intense  as  the  temperature  rises. 

257.  Different  Kinds  of  Radiation. — At   low  tempera- 
tures bodies  emit  only  obscure  radiations.     When  the  tem- 
perature reaches  a  certain  point,  the  body  becomes  red- 
hot,  and  begins  to  emit  luminous  radiations.     At  a  still 
higher  temperature  it  becomes  white-hot. 

258.  Diathermanous  Bodies.  —  A  body,  like  air,  which 
will  allow  thermal  rays  to  pass  readily  through  it  is  said  to 
be  diathermanous.     If  a  polished  plate  of  glass  is  held  in 
front  of  a  body  heated  to  dull  redness,  it  will  stop  nearly 
all  the  heat  emitted  by  it.     If  the  same  plate  of  glass  is 
held  in  front  of  a  body  at  bright  white  heat,  it  will  allow 
considerable  heat  to  pass  through  it.     Glass  is  diatherma- 
nous to  luminous  radiations,  but  only  slightly  so  to  obscure 
thermal  radiations.     A  solution  of  alum  is  still  less  diather- 
manous to  obscure  thermal  rays,  although  it  allows  the  lumi- 
nous rays  to  pass  readily  through  it.     A  solution  of  iodine 
in    bisulphide    of    carbon,    on    the   contrary,   is   perfectly 
diathermanous  to  the  obscure  thermal  rays,  and  perfectly 
opaque  to  the  luminous  rays.     A  polished  plate  of  rock- 


202  NATURAL   PHILOSOPHY. 

salt  is  diathermanous  to  both  the  obscure  and  luminous 
rays. 

259.  The  Effect  of  Rise  of  Temperature  on  Radiation. — 
If  the  temperature  of  a  body  is  gradually  raised  to  the 
highest  possible  point,  and  a  cell  of  the  iodine  solution  is 
used  to  cut  off  the  luminous  radiations,  the  obscure  thermal 
radiations  will  be  found  to  grow  more  and  more  intense, 
both  before  and  after  the  body  begins  to  emit  luminous 
radiations.     A  rise  of  temperature,  then,  has  two  effects 
upon  the  radiation  of  a  body ;  it  causes  its  obscure  radia- 
tions to  become  more  intense,  and  gives  rise  to  new  radi- 
ations.    The  latter  radiations  differ  from  the  former  in 
having  quicker  vibrations  and  shorter  waves.     The  radia- 
tions of   longest  and   shortest  wave-lengths  are  obscure, 
while  those  of  medium  wave-lengths  are  luminous.     The 
radiations  of  all  wave-lengths  are  thermal,  but  the  thermal 
power  is  greatest  in  radiations  of  long  wave-lengths,  and 
least  in  those  of   short  wave-lengths.     All  radiations  are 
capable  of  producing  certain  chemical  effects,  but  this  chem- 
ical or  actinic  power  is  least  in  radiations  of  long  waves 
and  greatest  in  the  short  waves.     The  radiations  of  bodies 
have,  accordingly,  been  divided  into  three  classes  ;  namely, 
obscure  thermal,  luminous,  and  obscure  actinic.     At  low  tem- 
peratures bodies  emit  only  the  first  class  of  radiations ; 
at  higher  temperatures,  the  first  and  second  classes ;  and 
at  still  higher  temperatures,  all  three  classes. 

260.  Absorption.  —  Absorption  is  the  reverse  of  radiation. 
When  the  minute  waves  of  the  ether  encounter  the  mole- 
cules of  gross  matter,  they  throw  the  atoms  into  vibration, 
provided    these    can   vibrate   at   the    same    rate    as   the 
particles   of   the   ether    in    the   waves.     In  this  way   the 
rays  are  taken  up  and  absorbed  by  bodies.     It  is   only 
those  rays  which  are    absorbed  by  a  body  that  heat  it. 
Bodies  are  not  warmed   at  all  by   the   rays   which    they 
transmit. 


NATURAL   PHILOSOPHY.  203 

261.  Good  Radiators  are  Good  Absorbers.  —  Rough 
blackened  surfaces  are  better  radiators  than  smooth  pol- 
ished surfaces.  This  may  be  shown  by  the  following 
experiment.  Two  metallic  plates  A  and  B  (Figure  187) 
of  the  same  size  are  mounted  Fig.  187. 

on  standards  which  move  to 
and  fro  on  a  sliding  bar  at  the 
bottom.  Between  these  plates 
there  is  a  rod  for  supporting 
a  ball  at  the  height  of  the 
centre  of  the  plates.  A  is 
coated  with  polished  nickel 
on  both  sides,  and  B  with 
nickel  on  one  side  and  lampblack  on  the  other.  B  is 
made  to  turn  on  its  standard  so  that  the  surface  coated 
with  lampblack  may  be  turned  either  towards  the  ball  or 
from  it.  First,  turn  the  nickel  faces  of  the  plate  towards 
the  ball,  heat  the  ball  to  dull  redness,  place  it  upon  its 
rod,  and  move  both  plates  up  against  it  so  that  they  may 
be  heated  equally.  Place  a  differential  thermometer  as 
shown  in  the  figure,  so  that  its  bulbs  shall  be  equally  dis- 
tant from  the  two  plates.  One  of  the  bulbs  will  be  heated 
by  radiation  from  the  nickel  surface,  and  the  other  by  radia- 
tion from  the  blackened  surface.  The  liquid  in  the  stem 
will  move  towards  the  former  bulb,  showing  that  the  latter 
bulb  is  hotter,  and  that  the  radiation  is  more  powerful 
from  the  blackened  surface.  Now  reverse  plate  B,  turning 
its  blackened  face  towards  the  ball,  remove  the  ball,  and 
allow  both  plates  to  cool.  Place  each  plate  against  one 
of  the  bulbs  of  the  thermometer,  and  arrange  them  so  that 
they  shall  be  equally  distant  from  the  ball.  Heat  the  ball 
and  replace  it  on  the  rod.  The  plates  will  now  become 
heated  by  absorption  of  radiations  from  the  ball.  They 
will  receive  equal  radiations,  but  the  thermometer  will  in- 
dicate that  the  plate  with  the  lampblack  coating  towards 


204  NATURAL   PHILOSOPHY. 

the  ball  is  the  hotter.  Hence  the  blackened  surface  is 
the  better  absorber. 

Different  gases  as  well  as  different  solids  and  liquids 
differ  in  their  absorptive  power  and  in  the  kind  of  rays 
which  they  absorb.  Watery  vapor  among  gases  corre- 
sponds to  glass  among  solids  and  a  solution  of  alum  among 
liquids.  It  is  diathermanous  to  luminous  rays,  but  much 
less  so  to  obscure  rays. 

Stoves  and  radiators,  which  are  designed  to  give  out 
heat,  should  have  rough  blackened  surfaces ;  while  a  tea- 
pot, which  is  designed  to  keep  the  liquid  in  it  hot,  should 
have  a  bright  polished  surface. 

262.  Hot-Houses.  —  A  hot-house  is  a  structure  covered 
with  glass.  On  a  sunny  day  the  temperature  will  be  sev- 
eral degrees  higher  within  such  a  structure  than  on  the 
outside.  The  luminous  heat  which  comes  from  the  sun 
passes  readily  through  the  glass  and  falls  upon  the  objects 
within.  These  absorb  the  heat  and  in  turn  send  back 
obscure  heat.  This  heat  is  stopped  by  the  glass.  Hence 
the  heat  accumulates  within  the  hot-house.  A  hot-house 
may  be  described  as  a  trap  to  catch  sunbeams.  Even  at 
night  and  on  a  cold  cloudy  day  it  will  be  warmer  within  a 
hot-house  than  on  the  outside,  the  glass  preventing  the 
obscure  radiations  from  passing  off  into  space.  The 
watery  vapor  in  the  atmosphere  acts  just  like  the  glass  of 
the  hot-house. 


IV. 

LIGHT. 
A.   RADIATION. 

263.  Luminous  Bodies.  —  Bodies,  like  a  gas-jet  or  the 
sun,  which  emit  light  of  their  own,  are  said  to  be  luminous. 
Light  is  now  believed  to  originate  in  extremely  minute  and 
rapid  vibrations  of  the  atoms  of  matter.     These  vary  in 
rapidity  from  about  400  million  million  to  about  760  million 
million  a  second.     The  atoms  of  all  luminous  bodies  are 
supposed  to  be  vibrating  at  this  enormous  rate. 

When  a  body  is  heated  its  atoms  are  thrown  into  more 
and  more  rapid  vibrations,  and  when  their  rate  of  vibration 
reaches  400  million  million  a  second  the  body  begins  to 
become  luminous.  In  the  case  of  a  candle-flame  or  gas-jet, 
these  rapid  vibrations  are  produced  by  the  clashing  of 
the  atoms  of  oxygen,  hydrogen,  and  carbon  as  they  rush 
into  combination.  A  blacksmith  may  heat  a  nail  red-hot 
by  vigorously  hammering  it.  Each  blow  of  the  hammer 
throws  the  atoms  of  the  nail  into  more  rapid  vibration, 
till  they  finally  vibrate  fast  enough  to  develop  light. 

264.  Propagation  of  Light  by  the  Ether.  —  As  the  atoms 
of  matter  vibrate  in  the  ether  in  which  they  are  immersed, 
they  communicate  their  vibration  to   it.     The  vibrations 
thus  started  in  the  ether  are  propagated    through    it   in 
every  direction  in  minute  waves  and  with  an  inconceivable 
velocity.    These  ethereal  waves  vary  in  length  according  to 
the  rate  of  the  atomic  vibrations.    It  takes  somewhat  more 
than  35,000  of  the  longest  of  these  waves,  and  somewhat 


206  NATURAL   PHILOSOPHY. 

less  than  70,000  of  the  shortest  of  them,  to  make  the  length 
of  an  inch.  The  vibrations  are  transverse,  so  that  each 
luminous  wave  is  made  up  of  crest  and  hollow,  like  a  water- 
wave.  Light  and  luminous  radiations  are  the  same  thing. 
The  velocity  of  light  is  about  186,000  miles  a  second. 

265.  Velocity  of  Light.  — The  velocity  of  light  was  first 
determined  by  Roemer,  a  Danish  astronomer,  by  a  study 
of  the  eclipses  of  one  of  Jupiter's  moons.  He  found  by 
an  examination  of  a  long  series  of  observations  that  the 
mean  interval  between  two  successive  eclipses  of  the  moon 
was  about  42^  hours,  but  that  the  interval  varied  by 
a  regular  law,  according  to  the  motion  of  the  earth  with 
respect  to  Jupiter.  When  the  earth  was  moving  away 

Fig.  188. 


from  Jupiter,  from  T  to  T1  (Figure  188),  the  intervals 
were  longer  than  the  mean,  till  at  T1  the  eclipse  occurred 
about  16%  minutes  late;  and  these  intervals  were  longest 
when  the  earth  was  moving  away  from  Jupiter  most  rapidly. 
When  the  earth  was  again  moving  towards  Jupiter,  from 
T1  to  T,  the  intervals  were  shorter  than  the  mean,  and 
shortest  when  the  earth  was  moving  most  rapidly  towards 
Jupiter.  Now  we  cannot  be  aware  of  the  eclipse  till  the 
light  which  left  the  moon  just  as  it  entered  Jupiter's  shadow 
has  reached  the  earth ;  and  the  distance  this  light  has  to 


NATURAL   PHILOSOPHY.  207 

travel  is  continually  increasing  as  the  earth  travels  from 
T  to  T',  and  decreasing  as  the  earth  travels  from  T1  to 
T.  Roemer  concluded  that  this  must  be  the  reason  why 
the  intervals  between  the  eclipses  were  longer  than  the 
mean  in  the  one  case  and  shorter  in  the  other.  As  the 
eclipse  occurred  i6}4  minutes  .late  at  J1',  he  concluded  that 
it  must  take  light  about  16^  minutes  to  cross  the  earth's 
orbit.  As  this  distance  is  about  184,000,000  miles,  light 
must  travel  at  the  rate  of  about  186,000  miles  a  second. 
This  velocity  would  carry  light  around  the  earth  in  about  % 
of  a  second.  Great  as  is  this  velocity,  it  is  believed  that 
the  nearest  fixed  star  is  so  distant  that  it  would  take  light 
over  three  years  to  reach  us  from  it,  while  the  most  distant 
stars  are  at  least  a  thousand  times  more  remote. 

Were  all  the  stars  in  the  heavens  to  be  blotted  out  of  exist- 
ence to-night,  it  would  be  over  three  years  before  we  should 
miss  any  of  them,  a  quarter  of  a  century  before  we  should  miss 
many,  and  thousands  of  years  before  we  should  lose  them  all. 
The  light  which  will  enter  our  eyes  as  we  glance  at  some  star 
to-night  probably  started  on  its  journey  before  the  building  of 
the  great  pyramids,  and  has  been  travelling  8  times  the  distance 
around  the  earth  every  second  since. 

266.  Rectilinear  Propagation  of  Light.  —  When  sunlight 
enters  through  an  opening  into  a  darkened  room,  it  illu- 
mines the  dust  in  the  atmosphere  in  its  path,  which  may 
then  be  easily  traced.     This  path  is  always  found  to  be 
straight.     Light  always  traverses  a  homogeneous  medium 
in  straight  lines.     A  single  line  of  light  is  called  a  ray, 
and  a  collection  of  rays  a  beam. 

267.  Images  produced  by  Small  Apertures.  —  If  a  white 
screen  is  placed  opposite  a  small  opening  in  a  shutter  of 
a  darkened  room,  an  inverted  picture  of  the  outside  land- 
scape will  be  formed  on  the  screen,  all  the  movements 
and  colors  being  correctly  represented  (Figure  189).     The 
smaller  the  opening,  the  sharper  the  image. 


208 


NATURAL    PHILOSOPHY. 
'Fig.  .89. 


Fig.  190. 


The  formation  of  this  image  is  due  to  the  rectilinear 
propagation  of  light,  and  may  be  explained  by  means  of 
Figure  190.  The  point  A  is  sending 
out  rays  in  all  directions  in  straight 
lines.  The  rays  from  this  point  which 
pass  through  the  small  opening  must 
fall  upon  A1  of  the  screen.  In  the  same 
way,  the  rays  from  B  which  pass  through 
the  opening  must  fall  upon  B1.  As  A 
sends  light  to  no  part  of  the  screen 
except  A',  and  as  A  receives  Hght  from 
no  part  of  the  object  but  A,  the  color  and  brightness  of 
the  spot  A1  will  depend  upon  the  color  and  brightness 
of  A  ;  in  other  words,  A'  will  be  the  image  of  A.  In  like 
manner  B1  will  be  the  image  of  £,  while  the  points  of  the 
object  between  A  and  B  will  have  their  images  at  corre- 
sponding points  between  A  and  B'.  An  inverted  image 
of  A  B  will  thus  be  formed  between  A  and  B'. 

When  the  opening   is  large,  the  rays  passing  through 
each  point  of  it  will  form  an  image  on  the  screen.     These 


NATURAL   PHILOSOPHY.  209 

images  will  fall  upon  one  another,  but  will  not  exactly 
coincide.  Hence,  as  the  opening  is  enlarged,  the  image 
becomes  blurred,  until  finally  it  is  entirely  obliterated. 


A  similar  experiment  to  the  above  may  be  tried  by  hold- 
ing a  card  with  a  large  pin-hole  in  it  between  a  candle  and 
a  screen,  as  shown  in  Figure  191.  An  inverted  image  of 
the  candle  will  be  formed  on  the  screen. 

Fig.  192- 


When  the  sun  shines  through  a  small  hole  into  a  room 


210  NATURAL    PHILOSOPHY. 

with  the  blinds  closed,  no  matter  what  may  be  the  shape  of 
the  opening,  the  image  of  the  sun  formed  on  the  floor  or 
wall  will  be  round  or  oval,  according  as  it  falls  upon  a 
surface  which  is  perpendicular  or  oblique  to  the  rays 
(Figure  192). 

When  the  sun  shines  through  the  foliage  of  trees,  the 
spots  of  light  on  the  ground  will  always  be  round  or  oval, 
whatever  may  be  the  shape  of  the  openings  through  which 
the  sun  shines,  provided  they  are  sufficiently  small. 

When  the  sun  is  undergoing  eclipse,  the  progress  of  the 
eclipse  may  be  watched  by  noticing  the  shape  of  these 
spots,  which  will  always  be  that  of  the  uneclipsed  portion 
of  the  sun's  disc. 

268.  Shadows. —  Bodies  which,  like  glass,  will  allow 
light  to  pass  readily  through  them,  are  said  to  be  trans- 
parent. Bodies  which  will  not  allow  light  to  pass  through 
them  are  said  to  be  opaque. 

Owing  to  the  rectilinear  propagatipn  of  light,  opaque 
bodies  in  front  of  a  light  must  necessarily  shut  off  the 
light  from  some  of  the  space  behind  them.  In  doing  this 
they  are  said  to  cast  shadows. 

Fig.  193- 


If  the  luminous  body  S  (Figure  193)  is  a  mere  point,  the  body 
M  will  cast  a  well-defined  shadow  G  H  upon  the  screen  P '  Q. 
If  the  straight  line  S  G  is  kept  fast  at  S,  and  carried  round  the 
sphere  M,  touching  it  all  the  time,  it  will  describe  a  cone.  The 
part  MG,  as  it  passes  round,  will  exactly  mark  the  limits  of  the 
shadow  cast  by  M.  Whether  the  shadow  received  on  the  screen 
is  round  or  oval  will  depend  upon  whether  the  screen  is  perpen- 


NATURAL   PHILOSOPHY.  211 

dicular  or  oblique  to  the  axis  of  the  shadow.  If  the  luminous 
body  is  not  a  mere  point,  the  shadow  of  M  (Figure  194)  upon 
the  screen  will  be  indistinct  in  outline. 

Fig.  194. 


Prolong  the  line  G  S  to  A.  Keep  the  point  A  fixed  and  carry 
the  line  A  G  around  the  spheres  S  and  M,  keeping  it  all  the 
while  in  contact  with  both.  The  line  will  describe  a  cone 
which  will  touch  the  two  spheres  externally,  and  the  part  MG 
will  mark  out  the  space  from  which  the  light  is  entirely  ex- 
cluded. This  portion  is  called  the  umbra  of  the  shadow.  If 
the  line  S  C  is  kept  fixed  at  B,  and  then  carried  round  the  two 
spheres  so  as  to  be  kept  in  contact  with  both  of  them,  all  the 
time,  it  will  describe  a  double  cone,  whose  apex  will  be  at  B  and 
which  will  touch  the  two  spheres  internally.  The  part  NC  of 
this  line  will  mark  the  extreme  limits  of  the  shadow.  From  the 
portion  of  the  shadow  outside  of  the  umbra  only  a  portion  of  the 

Fig.  195. 


light  is  excluded,  and  the  farther  we  pass  from  the  umbra  the  less 
the  light  excluded.  This  portion  of  the  shadow  is  called  the 
penumbra.  It  will  be  seen  at  once  from  the  figure,  that 


212  NATURAL    PHILOSOPHY. 

the  light  from  S  will  reach  all  the  space  between  D  and  G,  and 
the  light  from  L  all  the  space  between  C  and  H. 

Suppose  a  luminous  body  (Figure  195)  placed  between  two 
opaque  bodies,  one  of  them  larger  and  the  other  smaller  than 
itself.  Conceive  a  cone  touching  the  luminous  body  and  either 
of  the  opaque  bodies  externally.  This  will  be  the  cone  of  total 
shadow,  or  the  cone  of  the  umbra.  All  points  within  it  are 
completely  excluded  from  view  of  the  luminous  body.  This 
cone  narrows  or  enlarges  as  it  recedes,  according  as  the  opaque 
body  is  smaller  or  larger  than  the  luminous  body.  In  the  former 
case,  it  terminates  at  a  finite  distance  ;  in  the  latter,  it  extends 
to  an  infinite  distance.  Now  conceive  a  double  cone  touching 
the  luminous  body  and  either  of  the  opaque  bodies  internally, 
This  cone  will  be  wider  than  the  cone  of  total  shadow,  and  will 
include  it.  It  is  called  the  cone  of  partial  shadow,  or  the  cone 
of  the  penumbra.  All  points  lying  within  it  are  excluded  from 
the  view  of  some  portion  of  the  luminous  body.  If  they  are 
nearer  its  outer  boundary,  they  are  very  slightly  shaded.  If 
they  are  so  far  within  it  as  to  be  near  the  total  shadow,  they  are 
almost  completely  shaded.  If,  therefore,  the  shadow  of  the 
opaque  body  is  received  on  a  screen,  it  will  not  have  sharply 
defined  edges,  but  will  show  a  gradual  transition  from  the  total 
shadow  of  the  central  portion  to  a  complete  absence  of  shadow 
at  the  outer  boundary  of  the  penumbra.  Thus  neither  the  edges 
of  the  umbra  nor  those  of  the  penumbra  are  sharply  defined. 

Fig.  196. 


269.  Illumination.  —  The  illuminating  power  of  a  source 
of  light  diminishes  as  the  square  of  the  distance  from  the 
illuminating  body  increases.  In  Figure  196  the  disc  CD 
is  held  parallel  with  the  screen  A  £,  and  half-way  between 


NATURAL  PHILOSOPHY. 


213 


the  screen  and  the  source  of  light  L.  The  diameter  of  the 
shadow  on  the  screen  will  be  twice  that  of  the  disc,  and  the 
area  of  the  shadow  four  times  that  of  the  disc.  The  disc 
receives  all  the  light  that  would  fall  upon  the  space  covered 
by  the  shadow,  were  the  disc  removed.  Hence  the  illumi- 
nation of  the  disc  is  four  times  as  intense  as  that  of  the 
screen.  If  the  disc  were  held  one  third  of  the  way  from  L  to 
the  screen,  the  area  of  the  disc  would  be  one  ninth  that  of 
its  shadow  on  the  screen,  and  the  illumination  of  the  disc 
would  be  nine  times  as  intense  as  that  of  the  screen. 

270.  Photometry.  —  Photometry  is  the  measurement  of  the 
relative  illuminating  power  of  different  sources  of  light. 
An  instrument  used  for  this  measurement  is  called  a  pho- 
tometer. Rumford's  photometer  is  one  of  the  simplest  of 
these  instruments.  Its  use  is  based  upon  the  comparison 
of  shadows.  An  opaque  rod  M  (Figure  197)  is  placed  in 

Fig.  .97. 


front  of  a  ground-glass  screen.  The  lights  Z  and  B  to 
be  compared  are  placed  so  that  each  casts  a  separate 
shadow  of  the  rod  upon  the  screen.  These  distances  are 
then  made  such  that  the  two  shadows  a  and  b  are  of  ex- 
actly the  same  intensity.  The  screen  must  then  be  receiv- 
ing the  same  illumination  from  each  light ;  for  the  shadow 
cast  by  B  is  illumined  by  Z,  and  that  cast  by  Z  is  illumined 
by  B.  Hence  the  illuminating  power  of  the  two  lights 


214  NATURAL    PHILOSOPHY. 

will  be  to  each  other  as  the  squares  of  the  distances  of  the 
lights  from  the  screen. 

B.    REFLECTION. 

271.  Diffusion. — When  light  meets  the  surface  of  a  new 
medium,  a  portion  of  it  is  thrown  back  and  scattered  irregu- 
larly in  every  direction.    This  light  is  said  to  be  diffused.    It 
is  by  means  of  the  light  thus  diffused  that  we  are  enabled 
to  see  the  surfaces  of  non-luminous  bodies.     Smooth  pol 
ished  surfaces  diffuse  less  light  than  rough  irregular  ones, 
but  the  most  highly  polished  mirror  diffuses  enough  light 
to   enable  us   to  see  its  surface,  though  sometimes  with 
difficulty. 

272.  Reflection.  —  On  meeting  the  surface  of  a  new  me- 
dium, a  portion  of  the  light  is  thrown  back  in  a  definite 

Fig.  I98.  direction.     This  light  is  said  to  be 

reflected.  In  Figure  198,  A  B  repre- 
sents the  surface  of  the  new  medium, 
1C  the  ray  coming  to  the  medium, 
or  the  incident  ray,  and  C R  the  re- 
flected ray.  P  C  \s  a  perpendicular  to  the  surface  of  the 
medium  at  the  point  C.  The  angle  1 C P  is  called  the 
angle  of  incidence,  and  the  angle  RCP'is  called  the  angle 
of  reflection. 

In  reflection,  the  angles  of  incidence  and  reflection  are 
always  equal  to  each  other.  The  smoother  the  surface  of 
a  medium,  the  greater  the  proportion  of  the  light  reflected 
from  it.  Good  reflecting  surfaces  are  called  mirrors. 

273.  Images  formed  by  Plane  Mirrors.  —  It    is    by  re- 
flected light  that  we  see  objects  mirrored  in  reflecting  sur- 
faces.    The  reflecting  surface   is  said   to  form  images  of 
the  object.      These  visible  images  of  objects  formed  by 
reflection  correspond  to  the  echoes  formed  by  reflection  in 
the  case  of  sound. 

Figure  199  represents  a  pencil  of  rays  emitted  from  the 


NATURAL    PHILOSOPHY. 


2IS 


highest  point  of  a  candle-flame  to  the  eye  of  an  observer. 
The  rays  have  exactly  the  Fig.  199. 

same  degree  of  divergence 
after  reflection  as  before, 
and  if  prolonged  back- 
ward would  meet  just  as 
far  behind  the  mirror  as 
the  point  from  which  they 
come  is  in  front  of  it.  The 
same  would  be  true  of  the 
rays  coming  from  every  point  of  the  object.  Hence  an 
image  seen  in  a  plane  mirror  will  seem  just  as  far  behind 
the  mirror  as  the  object  is  in  front  of  it.  This  is  not  only 
true  of  the  image  as  a  whole,  but  also  of  each  part  of  the 
image.  If  the  object  is  parallel  with  the  surface  of  the 
mirror,  the  image  will  appear  parallel  with  the  surface  of 
the  mirror  ;  if  the  object  is  at  any  angle  to  the  surface  of 
the  mirror,  the  image  will  appear  at  the  same  angle  to  the 
surface  of  the  mirror  on  the  other  side,  each  point  of  the 
image  appearing  just  as  far  behind  the  mirror  as  the  cor- 
responding point  of  the  object  is  in  front  of  it. 

274.  Multiple  Images  formed  by  two  Parallel  Plane  Mir- 
rors—  When  an  object  Fig.  200. 
O  is  placed  between  two 
parallel  plane  mirrors 
(Figure  200),  the  rays  of 
light  from  it  may  reach 
the  eye  after  one,  two,  or 
three  reflections.  The 
rays  which  reach  the  eye 
after  one  reflection  from 
the  upper  mirror  would 
form  the  image  av  and 
those  that  reach  the  eye 
after  one  reflection  from 


2i6  NATURAL  PHILOSOPHY. 

the  lower  mirror  would  form  the  image  ov  The  rays  which 
reach  the  eye  after  two  reflections,  one  from  each  mir- 
ror, would  form  the  images  0.2  and  a.2 ;  and  those  which 
reach  the  eye  after  three  reflections,  the  images  as  and  oy 
In  the  figure,  only  those  rays  are  represented  which  reach 
the  eye  after  three  reflections. 

Fig.  201. 


275.  Images  formed  by  two  Mirrors  at  an  Angle  to  each 
other.  —  Figure  201  shows  the  images  that  would  be 
formed  by  two  mirrors  at  right  angles  to  each  other,  one 
being  horizontal  and  the  other  vertical. 

Figure  202  shows  the  images  that  would  be  formed   if 
an  object  were  placed  between  two   mirrors  facing  each 
Fig.  202.  other  at  an  angle  of  60°.     When 

the  mirrors  are  inclined  to  each 
other,  the  images  that  are  formed 
by  multiple  reflections  are  always 
arranged  in  the  circumference  of 
a  circle,  whose  centre  is  at  the 
intersection  of  the  two  mirrors, 
and  whose  circumference  passes 
through  the  object. 

276.    The  Kaleidoscope.  —  The 


NATURAL  PHILOSOPHY. 


417 


kaleidoscope  is  an  optical  toy,  invented  by  Sir  David 
Brewster.  It  consists  of  a  tube  containing  two  glass 
plates,  extending  along  its  whole  length,  and  inclined 
at  an  angle  of  60°.  One  end  of  the  tube  is  closed  by 
a  metal  plate,  with  the  exception  of  a  hole  in  the  cen- 
tre, through  which  the  Fig.  203. 
observer  looks  in  ;  at  the 
other  end  there  are  two 
plates,  one  of  ground  and 
the  other  of  clear  glass 
(the  latter  being  next  the 
eye),  with  a  number  of 
little  pieces  of  colored 
glass  lying  loosely  be- 
tween them.  These  col- 
ored objects,  together  with 
their  images  in  the  mir- 
rors, form  symmetrical 
patterns  of  great  beauty,  which  can  be  varied  by  turning 
or  shaking  the  tube,  so  as  to  cause  the  pieces  of  glass 
to  change  their  positions  (Figure  203). 

A  third  reflecting  plate  is  sometimes  employed,  the  cross- 
section  of  the  three  forming  an  equilateral  triangle.  As 
each  pair  of  plates  produces  a  kaleidoscopic  pattern,  the 
arrangement  is  nearly  equivalent  to  a  combination  of  three 
kaleidoscopes. 

The  kaleidoscope  is  capable  of  rendering  important  aid 
to  designers. 

C.    REFRACTION. 

277.  Illustration  of  Refraction.  —  If  abeam  of  light  is 
allowed  to  fall  obliquely  upon  water,  it  will  be  seen  to  be 
bent  on  entering  the  water,  though  it  will  continue  to  move 
on  in  a  straight  line  after  it  has  passed  into  the  water.  This 
bending  of  a  ray  of  light,  on  passing  obliquely  from  one 
medium  to  another,  is  called  refraction. 


2l8 


NATURAL   PHILOSOPHY. 


If  a  coin  or  other  object  m  n  (Figure  204)  is  placed  on 
Fig-  204-  the   bottom    of    a  vessel 

with  opaque  sides,  so  as 
just  to  be  concealed  from 
.^^  an  eye  at  O,  and  the  ves- 

L J$&//\  sel  is  then  filled  with 

*^ts  water,  the  bottom  of  the 

P  *»£>  II  vessel  will   seem  to  rise 

and  the  object  will  come  into  view.  This  is  because  the 
pencils  of  rays  coming  from  the  object  at  m  will  be  sud- 
denly bent  on  entering  the  air, 
and  will  reach  the  eye  as  if  they 
came  from  ;;/',  where  the  object 
will  appear  to  be. 

For  a  similar  reason,  a  stick 
partly  immersed  in  water,  in 
an  oblique  position,  will  ap- 
pear bent,  as  shown  in  Figure 
205. 

Two  Cases  of  Refraction.  —  When  a  ray  of  light 
passes  obliquely  from  a  rarer  into  a  denser  medium,  it  is 
bent  towards  a  perpendicular  drawn  to  the  surface  of  the 
medium  at  the  point  of  contact  of  the  ray.  In  Figure  206, 
A  B  represents  the  surface  of  a  denser  medium,  1C  the 
incident  ray,  CR  the  refracted  ray,  and  P  C H a  perpen- 
dicular to  the  surface  of  the  medium  at  the  point  C.  The 


Fig.  206. 


Fig.  207. 
IP 


angle  R  C  H  is  the  angle  of  refraction.     In  this  case  the 
angle  of  refraction  is  less  than  the  angle  of  incidence. 


NATURAL    PHILOSOPHY.  219 

When  a  ray  of  light  enters  a  rarer  medium  obliquely,  it 
is  bent  from  a  perpendicular  to  the  surface  of  the  medium 
at  the  point  of  contact.  In  Figure  207,  A  B  represents 
the  surface  of  a  rarer  medium,  1C  the  incident  ray,  C R 
the  refracted  ray,  and  PCffthe  perpendicular.  In  this 
case  the  angle  of  refraction  is  greater  than  the  angle  of 
incidence. 

When  a  ray  of  light  enters  any  medium  perpendicularly, 
there  is  no  refraction. 

279.  Law  of  Refraction.  —  In  Figure  208,  A  B  represents  the 
surface  of  a  denser  medium,  1C  the  incident  ray,  C  R  the  re- 
fracted ray,  P  C  H  the  perpendicu- 
lar to  the  surface  of  the  medium 

at  the  point  of  the  contact  of  the 
ray.  A  circle  of  any  radius  is 
described  about  the  point  C  as  a 
centre,  and  from  the  points  D  and 
/''where  this  circle  cuts  the  inci- 
dent and  refracted  rays,  the  lines 
D  E  and  FG  are  drawn  at  right 
angles  to  the  perpendicular  P  C  H.  These  lines  are  called  the 
sines  of  the  angles  ICP  and  R  C  H,  respectively.  The  law 
of  refraction  is  this :  If  the  size  of  the  angle  of  incidence  is 
changed,  the  size  of  the  angle  of  refraction  will  change  in  such  a 
way  that  the  length  of  the  lines  D  E  and  FG  will  change  at  the 
same  rate.  As  one  increases  in  length,  the  other  increases  in 
length  and  at  the  same  rate,  and  vice  versa.  This  law  is  usually 
stated  as  follows  :  For  the  same  media  the  sines  of  the  angles  of 
incidence  and  of  refraction  always  bear  the  same  ratio.  This  ratio 
is  called  the  index  of  refraction  for  the  media.  When  light  is 
passing  from  air  to  glass  the  sines  of  these  angles  are  as  3  to  2; 
and  from  air  to  water,  as  4  to  3.  The  index  of  refraction  for  the 
former  media  is  -f  and  for  the  latter  J. 

280.  Total  Reflection.  —  The    angle   of    incidence   may 
have  any  value  from  o°  up  to  90°.     When  light  enters  a 
denser  medium,  the  angle  of  refraction   is  less  than  the 
angle  of  incidence,  and  hence  always  less  than  90°.     But 


NATURAL  PHILOSOPHY. 


Fig.  209.  when  light  enters  a  rarer  medium, 

there  is  always  a  certain  angle  of 
incidence  1C P  (Figure  209)  at 
Ba  which  the  angle  of  refraction 
H  CR  is  equal  to  90°.  This  angle 
is  called  the  limiting  angle,  or  the 
critical  angle.  When  the  media  are  air  and  water,  this  angle 
is  about  48^  degrees.  For  air  and  the  different  kinds  of 
glass  it  ranges  from  38°  to  41°. 

When  the  angle  of  incidence  exceeds  the  limiting  angle, 
Fig.  210.  none  of    the  light  will 

enter  the  medium,  how- 
ever transparent  it  may 
be.  In  this  case  the 
light  will  be  totally  re- 
flected, the  angle  of  re- 
flection being  equal  to 
that  of  incidence. 

If  a  glass  of  water, 
with  a  spoon  in  it,  is 
held  above  the  level  of 
the  eye  (Figure  210), 
the  under  side  of  the 
surface  of  the  water  is 
seen  to  shine  like  pol- 
ished silver,  and  the 
lower  part  of  the  spoon 
is  seen  reflected  in  it. 
The  rays  of  light  which 
pass  upward  through 
the  water  at  a  certain 
angle  are  totally  reflected  on  meeting  the  air. 

28 1 .  Path  of  a  Ray  through  a  Rectangular  Prism  of  Glass. 
—  By  a  rectangular  prism  in  optics  is  meant  a  prism  whose 
base  is  an  isosceles  right-angled  triangle. 


NATURAL    PHILOSOPHY. 


Suppose  a  ray  of  light  1C  (Figure  211)  to 
meet  one  of  the  narrower  sides  n  o  of  the  rec- 
tangular prism  m  n  o  perpendicularly.  At  D  it 
will  be  totally  reflected,  since  it  will  meet  the 
air  at  the  angle  of  incidence  C  D  P  equal  to  45°. 
At  E  it  will  pass  out  of  the  prism  without  bend- 
ing because  it  will  meet  the  surface  perpendicu- 
larly. This  ray  will  be  totally  reflected  once 
and  turned  90°  out  of  its  original  course.  All 
the  angles  in  the  figure  marked  with  a  small 
circle  are  right  angles,  and  those  marked  with  a  cross  are  angles 
of  45°. 

Suppose  the  incident  ray  /  C  (Figure  212)  to  meet  the  broader 
side  m  n  of.  the  prism  perpendicularly.  It  will  enter  without 
bending  since  it  meets  the  surface  Fig.  212. 

perpendicularly.  At  D  it  will  be 
totally  reflected,  since  it  meets  the 
air  at  an  angle  of  45°.  At  E  it  will 
again  be  totally  reflected,  since  it 
again  meets  the  air  at  an  angle  of  45°. 
At  F  it  will  leave  the  prism  without 
bending,  since  it  meets  the  surface 
perpendicularly.  In  this  case  the  ray 
is  totally  reflected  twice,  and  turned 
180°  from  its  original  course.  The  angles  in  this  figure  are 
marked  as  before.  By  means  of  a  total-reflecting  prism,  the 
direction  of  rays  of  light  may  be  changed  without  loss  of  light. 

282.    Path  of  a  Ray  through  a  Dense  Medium  with  Par- 
allel Sides. —  In  Figure  213,  m  n  and  op  represent  the  par- 
allel sides  of  some  dense  medium,  as  Fig 
glass.     1C  represents  the  ray  com- 
ing to  the  first  surface,  and  C B  is 
the  prolongation  of  the  direction  of 
the  incident  ray.     On  entering   the 
medium,  the  ray  is  bent  towards  the 
perpendicular  P  C  ff,  and  on  leaving 
the  medium  at  A  it  is  bent  from  the 


NATURAL    PHILOSOPHY. 


perpendicular  E  D  F.  The  second  bending  is  equal  to 
the  first  and  in  the  opposite  direction,  so  that  the  ray  D  R 
emerges  from  the  medium  with  the  same  direction  it  had 
before  entering  the  medium.  Had  the  ray  started  from  R 
and  met  the  medium  at  Z>,  it  would  have  taken  the  same 
path  back  through  the  medium,  and  have  emerged  with 
the  direction  C  I.  This  is  only  one  case  of  the  general 
law  that  the  course  of  the  returning  ray  is  the  same  as  that 
of  the  direct  ray. 

283.  Path  of  a  Ray  through  a  Dense  Medium  with  In- 
dined  Sides.  —  Whenever  a  ray  of  light  traverses  a  denser 
medium  with  inclined  sides,  it  will  be  turned  aside  towards 
the  thicker  part  of  the  medium. 

In  Figure  214,  the  ray  I C  D  R  is  represented  as  passing 
through  the  medium  in .  such  a  way  as  to  be  bent  twice, 
once  at  C  towards  the  thicker  part 
of  the  medium,  and  once  at  D 
towards  the  thinner  part.  In  every 
such  case  the  bending  towards  the 
thicker  part  of  the  medium  will  be 
greater  than  that  towards  the  thinner 
part.  Hence  the  resultant  deviation 
of  the  ray  from  its  original  course 
will  be  towards  the  thicker  part  of  the  medium. 

In  Figure  215,  the  ray  is  represented  as  passing  through 

Fig.  2.5.  Fig.  216. 

TV  T- 


H' 


\ 


AD  \ 
I  \\ 


the  medium  in  such  a  way  as  to  be  bent  only  once,  since 
it  meets  one  side  of  the  medium  perpendicularly.     In  this 


NATURAL   PHILOSOPHY.  223 

case  the  bending  will  be  always  towards  the  thicker  part 
of  the  medium. 

In  Figure  216  the  ray  is  represented  as  passing  through 
the  medium  in  such  a  way  as  to  be  bent  twice,  both  times 
towards  the  thicker  part  of  the  medium.  In  all  three 
cases  the  path  of  the  ray  would  be  the  same,  whether  the 
ray  starts  from  7  or  J?. 

D.   DISPERSION. 

284.  The  Dispersion  Spectrum.  —  If  a  glass  prism  is 
held  with  its  edge  down  in  the  path  of  a  thin  beam  of 
light,  the  spot  of  light  on  the  screen  will  be  raised  and  be 

Fig.  217. 


changed  into  a  beautifully  colored  band,  in  which  the 
colors  are  arranged  in  the  order  of  red,  orange,  yellow, 
green,  blue,  indigo,  and  violet.  The  colored  band  produced 
by  the  passage  of  a  beam  of  light  through  a  prism  is  called 
the  dispersion  spectrum.  The  raising  of  the  spot  of  light 
on  the  screen  is  due  to  the  bending  of  the  beam  as  a  whole 
towards  the  thicker  part  of  the  medium  ;  and  the  forma- 
tion of  the  colored  band,  to  the  unequal  bending  of  the 
different  colored  rays  of  which  white  light  is  composed, 
red  being  bent  the  least  and  violet  the  most  of  all  the  rays. 
The  separation  of  the  colored  rays  by  refraction  is  called 
dispersion.  The  action  of  the  prism  on  the  rays  is  shown 
in  Figure  217. 


224  NATURAL   PHILOSOPHY. 

The  refrangibility  of  light  is  found  to  depend  upon  the 
length  of  its  waves ;  the  shorter  the  waves,  the  more  re- 
frangible the  ray.  The  violet  rays  are  more  refrangible 
than  the  red  because  they  have  shorter  waves. 

In  the  case  of  sunlight  and  of  light  from  any  intense 
source  of  heat,  it  is  found  that  the  thermal  power  of  the 
spectrum  extends  considerably  beyond  the  red,  and  the 
chemical  power  considerably  beyond  the  violet.  The  com- 
plete spectrum  is  composed  of  three  parts,  a  luminous 
portion  at  the  centre,  an  obscure  thermal  portion  beyond  the 
red,  and  an  obscure  actinic  portion  beyond  the  violet.  Every 
portion  of  the  spectrum  is  thermal,  but  the  thermal  power 
increases  rapidly  as  we  approach  the  red  end,  and  is  great- 
est in  the  region  just  beyond  the  red.  Every  part  of  the 
spectrum  is  also  actinic,  but  the  greatest  actinic  power  is  in 
the  region  of  the  blue.  Only  the  central  part  of  the  spec- 
trum is  luminous,  and  the  greatest  luminosity  is  in  the 
region  of  the  yellow  and' green. 

285.  Achromatic  and  Direct-  Vision  Prisms.  — The  refrac- 
tive power  of  a  substance  is  independent  of  its  dispersive 
power.  Hence,  by  using  different  kinds  of  glass,  it  has 
been  found  possible  to  construct  prisms  which  shall  have 
equal  refractive  and  unequal  dispersive  powers,  or  equal 
dispersive  and  unequal  refractive  powers.  If  two  prisms  of 
crown  and  flint  glass  are  constructed  so  as  to  have  equal 
powers  of  bending  a  beam  of  light  as  a  whole,  the  flint-glass 
prism  will  produce  greater  dispersion  than  the  crown-glass. 
If,  on  the  other  hand,  the  two  prisms  are  constructed  so  as 
to  produce  equal  dispersion,  the  crown-glass  prism  will 
bend  the  ray  as  a  whole  more  than  the  flint-glass. 

The  refractive  and  dispersive  powers  of  a  prism  both 
increase  with  the  inclination  of  its  sides.  When  two  prisms 
of  equal  dispersive  and  unequal  refractive  powers  are  com- 
bined, with  the  thicker  part  of  one  beside  the  thinner  part 
of  the  other  (Figure  218),  they  form  what  is  called  an 


NATURAL   PHILOSOPHY. 


225 


Fig. 


achromatic  prism.  Such  a  prism  will  produce  refraction 
without  dispersion.  Achromatic  means  without  color. 

When  two  prisms  of  equal  re- 
fractive powers  and  unequal  dis- 
persive powers  are  combined  as 
above,  they  form  what  is  called  a 
direct-vision  prism.  Such  a  prism 
produces  dispersion  without  re- 
fraction. It  takes  its  name  from 
the  fact  that  in  using  it  you  look  ' 

directly  at  the  object  you  wish  to  examine,  while,  with  any 
other  prism,  you  are  obliged  to  look  somewhat  away  from 
the  object,  as  is  shown  in  Figure  219. 

Fig.  219. 


286.  The  Spectroscope.  —  The  spectroscope  is  an  instrument 
for  examining  spectra.  A  simple  spectroscope  is  shown  in 
Figure  220.  The  tube  at  the  right  is  called  the  eollimatol 
tube.  The  light  to  be  examined  is  admitted  through  3 
narrow  opening  at  the  end  of  the  tube,  and  the  rays  are 
rendered  parallel  by  means  of  a  lens  within  it.  The  light 
is  then  dispersed  by  the  prism,  and  the  spectrum  examined 


^226 


NATURAL   PHILOSOPHY. 


by  means  of  the  telescope  at  the  left  of  the  prism.     The 
tube  in  front  of  the  prism  has  a  scale  engraved  on  glass  in 

Fig.  220. 


the  opening  at  the  end  next  to  the  candle.     The  light  from 
Fig.  221.  the  candle  which  shines  through 

this  scale  is  reflected  from  the  side 
of  the  prism  into  the  telescope,  so 
as  to  form  an  image  of  the  scale 
alongside  that  of  the  spectrum. 
The  power  of  the  spectroscope 
may  be  increased  by  using  a  train 
of  prisms  to  disperse  the  light  in- 
stead of  a  single  prism.  The  ar- 
rangement of  the  prisms  is  shown 
in  Figure  221.  The  end  of  the 
collimator  tube  is  seen  at  the  left, 

and  that  of  the  telescope  at  the  right. 

A  direct-vision  spectroscope  is  one  in  which  direct-vision 

prisms  are  used. 

287.    Three  Kinds  of  Spectra.  —  If  we  examine  with  the 


NATURAL   PHILOSOPHY.  227 

spectroscope  the  light  from  an  incandescent  solid,  its  spec- 
trum will  be  found  to  be  a  continuous  band  of  colors, 
changing  by  insensible  gradations  from  red  at  one  end  to 
violet  at  the  other.  Such  a  spectrum  is  called  a  continuous 
spectrum.  Incandescent  solids  and  liquids  give  continu- 
ous spectra. 

If  we  examine  with  the  spectroscope  the  light  from  lumi- 
nous strontium  vapor,  its  spectrum  (see  frontispiece)  will 
be  seen  to  be  made  up  of  bright  lines  and  dark  spaces. 
Such  a  spectrum  is  called  a  bright-lined  or  broken  spectrum. 
Vapors  and  gases,  when  luminous,  give  bright-lined  spectra. 
The  spectra  of  different  gases  and  vapors  differ  in  the 
number  and  position  of  these  lines.  Hence  a  vapor  may 
be  recognized  by  its  spectrum. 

The  dark  spaces  of  these  spectra  are  due  to  the  absence 
of  certain  rays.  While  incandescent  solids  and  liquids 
emit  rays  of  all  degrees  of  refrangibility,  luminous  vapors 
and  gases  emit  those  only  of  particular  degrees  of  refrangi- 
bility. Each  vapor  or  gas  emits  just  as  many  sets  of  rays 
as  there  are  bright  lines  in  its  spectrum.  The  number  of 
these  lines  ranges  from  one  up  to  several  hundred.  The 
lines  of  the  spectrum  of  a  vapor  change  somewhat  with  the 
temperature  of  the  vapor.  The  analysis  of  light  by  means 
of  the  spectroscope  is  called  spectrum  analysis. 

The  spectrum  of  an  incandescent  solid  or  liquid,  when 
shining  through  a  luminous  vapor  or  gas,  is  made  up  of 
dark  lines  separated  by  bright  spaces,  there  being  a  dark 
line  for  every  bright  line  which  the  gas  alone  would  give. 
Such  spectra  are  called  reversed  spectra,  the  spectrum  of  the 
gas  being  reversed  by  the  light  of  the  solid  which  passes 
through  it. 

288.  Explanation  *>f  Reversed  Spectra. —  It  has  been  found 
that  gases  absorb  and  quench  rays  of  the  same  degree  of  refrangi- 
bility as  those  which  they  themselves  emit,  and  no  others.  When 
a  solid  is  shining  through  a  luminous  vapor,  this  absorbs  and 


228  NATURAL   PHILOSOPHY. 

quenches  those  rays  from  the  solid  which  have  the  same  degrees 
of  refrangibility  as  those  which  it  is  itself  emitting.  Hence  the 
lines  of  the  spectrum  receive  light  from  the  vapor  alone,  while 
the  spaces  between  the  lines  receive  light  from  the  solid.  Now 
solids  and  liquids  when  heated  to  incandescence  give  a  very 
much  brighter  light  than  vapors  and  gases  at  the  same  tempera- 
ture. Hence  the  lines  of  a  reversed  spectrum,  though  receiving 
light  from  the  vapor  or  gas,  appear  dark  by  contrast. 

289.  The  Molecular  Theory  of  Radiation.  —  The  following 
account  of  the  molecular  theory  of  radiation  is  taken  from  Max- 
well's "  Molecular  Theory  of  Heat :  "  — 

"  If  the  parts  of  the  molecule  are  capable  of  relative  motion 
without  being  altogether  torn  asunder,  this  relative  motion  will 
be  some  kind  of  vibration.  The  small  vibrations  of  a  connected 
system  may  be  resolved  into  a  number  of  simple  vibrations,  the 
law  of  each  of  which  is  similar  to  that  of  a  pendulum.  It  is 
probable  that  in  gases  the  molecules  may  execute  many  of  such 
vibrations  in  the  interval  between  successive  encounters.  At 
each  encounter  the  whole  molecule  is  roughly  shaken.  During 
its  free  path  it  vibrates  according  to  its  own  laws,  the  amplitudes 
of  the  different  simple  vibrations  being  determined  by  the  nature 
of  the  collision,  but  their  periods  depending  only  on  the  consti- 
tution of  the  molecule  itself.  If  the  molecule  is  capable  of 
communicating  these  vibrations  to  the  medium  in  which  radi- 
ations are  propagated,  it  will  send  forth  radiations  of  certain 
definite  kinds,  and  if  these  belong  to  the  luminous  part  of  the 
spectrum,  they  will  be  visible  as  light  of  definite  refrangibility. 
This,  then,  is  the  explanation,  on  the  molecular  theory,  of  the 
bright  lines  observed  in  the  spectra  of  incandescent  gases. 
They  represent  the  disturbance  communicated  to  the  luminifer- 
ous  medium  by  molecules  vibrating  in  a  regular  and  periodic 
manner  during  their  free  paths.  If  the  free  path  is  long,  the 
molecule,  by  communicating  its  vibrations  to  the  ether,  will 
cease  to  vibrate  till  it  encounters  some  other  molecule. 

"  By  raising  the  temperature  we  increase  the  velocity  of  the 
motion  of  agitation  and  the  force  of  each  Encounter.  The  higher 
the  temperature  the  greater  will  be  the  amplitude  of  the  internal 
vibrations  of  all  kinds,  and  the  more  likelihood  will  there  be  that 
vibrations  of  short  period  will  be  excited,  as  well  as  those  funda- 


NATURAL   PHILOSOPHY. 


229 


mental  vibrations  which  are  most  easily  produced.  By  increas- 
ing the  density  we  diminish  the  length  of  the  free  path  of  each 
molecule,  and  thus  allow  less  time  for  the  vibrations  excited  at 
each  encounter  to  subside  ;  and  since  each  fresh  encounter  dis- 
turbs the  regularity  of  the  series  of  vibrations,  the  radiations  will 
no  longer  be  capable  of  complete  resolution  into  a  series  of 
vibrations  of  regular  periods,  but  will  be  analyzed  into  a  spec- 
trum showing  the  bright  bands  due  to  the  regular  vibrations, 
along  with  a  ground  of  diffused  light,  forming  a  continuous 
spectrum  due  to  the  irregular  motion  introduced  at  each  en- 
counter. 

"  Hence,  when  a  gas  is  rare,  the  bright  lines  of  its  spectrum 
are  narrow  and  distinct,  and  the  spaces  between  them  are  dark. 
As  the  density  of  the  gas  increases,  the  bright  lines  become 
broader,  and  the  spaces  between  them  more  luminous. 

"When  the  gas  is  so  far  condensed  that  it  assumes  the  liquid 
or  solid  form,  then,  as  the  molecules  have  no  free  path,  they 
have  no  regular  vibrations,  and  no  bright  lines  are  commonly 
observed." 

E.  LENSES. 

290.  Forms  of  Lenses.  —  A  lens  is  a  transparent  me- 
dium having  at  least  one  curved  side.  Lenses  are  usually 


made  of  glass,  and  are  circular  in  outline.  Their  curved 
surfaces  are  usually  spherical.  They  are  divided  into  two 
classes,  according  to  their  shape,  namely,  convex  lenses  and 
concave  lenses.  Every  convex  lens  has  at  least  one  convex 
surface,  and  is  thickest  at  the  centre ;  and  every  concave 
lens  has  at  least  one  concave  surface,  and  is  thickest  at  the 


230 


NATURAL   PHILOSOPHY. 


margin.  There  are  three  forms  of  each  class  of  lenses. 
These  six  forms  of  lenses  are  shown  in  section  in  Figure 
222.  The  first  three  are  convex  and  the  last  three  con- 
cave lenses.  A  is  a  double-convex  lens,  having  two  convex 
surfaces.  B  is  a  plano-convex  lens,  having  one  plane  and 
one  convex  surface.  C  is  a  concavo-convex  lens,  having  a 
concave  and  a  convex  surface,  the  convex  surface  having 
the  greater  curvature.  This  lens  is  often  called  a  meniscus. 
D  is  a  double-concave  lens,  having  two  concave  surfaces. 
E  is  a  plano-concave  lens,  having  a  plane  and  a  concave 
surface.  F  is  a  convexo-concave  lens,  having  a  convex  and 
a  concave  surface,  the  concave  surface  having  the  greater 
curvature. 

291.  Optical  Centre  of  Lenses.  —  There  is  for  every  lens 
a  certain  point,  any  straight  line  drawn  through  which  will 
meet  on  opposite  sides  of  the  lens  portions  of  surface 
which  are  parallel  to  each  other.  The  point  is  called  the 
optical  centre  of  the  lens. 

The  optical  centre  of  any  lens  with  two  curved  surfaces  may 


Fig.  223. 


be  found  by  the  following  con- 
struction. In  Figure  223,  A  and 
B  are  the  centres  of  the  two  sur- 
faces of  the  lens  mp  o  and  tn  n  o. 
From  A  draw  any  radius  A  C, 
and  from  B  draw  the  radius  B  D 
parallel  to  A  C.  Join  the  points  A 
and  Z?,  and  Cand  D  with  straight 
lines.  The  point  O  where  these  lines  cross  will  be  the  optical 
centre  of  the  lens.  The  portions  of  surface  at  C  and  D  will  be 
parallel  to  each  other,  since  each 
will  be  perpendicular  to  the  radius 
drawn  to  that  point,  and  these 
radii  are  parallel  to  each  other. 
If  any  straight  line  whatever  were 
drawn  through  O,  the  points  of 
surface  where  this  line  intersects 
the  sides  of  the  lens  would  be  parallel  to  each  other. 


NATURAL    PHILOSOPHY.  231 

Figure  224  shows  the  same  method  applied  to  a  double-con- 
cave lens.  In  the  case  of  a  double-convex  and  a  double-concave 
lens  the  optical  centre  is  within  the  lens. 

Fig.  225.  Fig.  226. 


Figures  225  and  226  show  the  above  method  applied  to  a 
concavo-convex  lens  and  to  a  convexo-concave  lens.  In  these 
cases  the  optical  centre  is  without  the  lens  on  the  side  of  the 
greater  curvature. 

The  optical  centre  of  a  plane  lens  is  at  the  middle  point  of 

Fig.  227.  Fig.  228. 


its  curved  surface.  This  is  evident  from  Figures  227  and  228. 
The  radius  A  O  drawn  to  the  middle  point  of  the  curved  sur- 
face m  Op  will  be  perpendicular  to  the  plane  side  at  the  point  «, 
and  to  the  curved  surface  at  O,  for  a  radius  drawn  to  the  middle 
point  of  an  arc  is  perpendicular  to  the  chord  of  the  arc,  or  to  a 
line  parallel  with  it  Hence  the  point  of  the  surface  at  O  is 
parallel  to  every  portion  of  the  plane  side.  Therefore  any 
straight  line  drawn  through  O  would  meet  on  opposite  sides  of 
the  lens  portions  of  surface  parallel  to  each  other. 

292.  Axes  and  Foci  of  Lenses.  —  Any  straight  line  drawn 
through  the  optical  centre  of  a  lens  is  called  an  axis.  An 
axis  which  passes  through  the  centre  of  curvature  of  a  lens 
is  called  the  principal  axis,  and  every  other  axis  a  second- 
ary axis.  Every  ray  of  light  which  coincides  with  an  axis 
will  emerge  from  a  lens  with  the  same  direction  it  had 
before  entering,  since  it  will  pass  through  a  portion  of 


232  NATURAL   PHILOSOPHY. 

a  medium  having  parallel  sides.  Every  other  ray  which 
passes  through  a  lens  will  be  deflected  towards  the  thicker 
part  of  the  lens,  since  it  will  pass  through  a  portion  of  a 
medium  having  inclined  sides.  In  the  case  of  a  convex 
lens  the  deflection  will  be  towards  the  centre  of  the  lens, 
and  of  a  concave  lens  towards  the  margin. 

When  the  rays,  on  emerging  from  a  lens,  are  either 
convergent  or  divergent,  the  points  towards  which  they 
converge  or  from  which  they  diverge  are  called  foci. 
When  the  rays  are  convergent  on  emerging  from  the  lens, 
the  focus  is  real ;  and  when  they  are  divergent,  virtual. 

Fig.  229.  Fig.  230. 


293.  Parallel  Rays  with  Lenses.  — Figure  229  represents  the 
case  of  parallel  rays  with  a  convex  lens  when  the  rays  are  par- 
allel to  the  principal  axis  and  lie  on  opposite  sides  of  it.  The 
lens  being  thickest  at  the  centre,  the  rays  are  deflected  towards 
the  axis,  and  so  become  convergent  and  meet  at  the  point  F. 

Figure  230  shows  the  case  of  parallel  rays  with  a  convex  lens 
when  the  rays  are  parallel  with  the  principal  axis  and  are  on 
the  same  side  of  it.  The  rays  are  both  deflected  towards  the 
axis  and  made  convergent,  because  the  marginal  ray  is  deflected 
more  than  the  central  one,  the  inclination  of  the  sides  of  the 
lens  becoming  greater  and  greater  as  we  pass  from  the  centre 
of  the  lens  to  the  margin. 

Fj    2  T  Figure  231  shows  the  case  of  parallel 

rays  with  a  convex  lens  when  the  rays 
are  parallel  with  a  secondary  axis  and 
lie  on  the  same  side  of  it. 

Parallel  rays  with  a  convex  lens 
become  convergent  on  emerging  from 
the  lens,  and  have  a  real  focus,  on  the  opposite  side  of 


NATURAL    PHILOSOPHY. 


233 


Fig.  233. 


the  lens  to  that  on  which  they  enter,  and  on  the  axis  to 
which  the  rays  are  parallel. 

Figure     232     represents  Fig.  232. 

the  case  of  parallel  rays 
with  a  concave  lens  when 
the  rays  are  parallel  with 
the  principal  axis  and  lie 
on  opposite  sides  of  it. 
The  rays  are  deflected  from 
the  axis,  because  the  lens 
is  thickest  at  the  margin,  and  so  become  divergent,  with  F  as 
their  point  of  divergence. 

Figure  233  represents  the 
case  of  parallel  rays  with  a 
concave  lens  when  the  rays  are 
parallel  with  the  principal  axis 
and  lie  on  the  same  side  of  it. 
The  rays  are  deflected  from  the 
axis,  and  the  marginal  ray  is 

deflected  more  than  the  central  one,  because  of  the  greater 
inclination  of  the  sides  towards  the  margin  ;  and  because  of  the 
greater  deflection  of  the  marginal  ray  the  rays  become  divergent, 
with  their  point  of  divergence  at  F. 

Parallel  rays  with  a  concave  lens  become  divergent,  and 
have  a  virtual  focus  on  the  same  side  of  the  lens  as  that 
on  which  the  rays  enter  and  on  the  axis  to  which  the  rays 
are  parallel. 

294.  Principal  Foci  and  Focal  Length.  —  The  focus  for 
parallel  rays  is  called  the  principal  focus  of  the  lens.     It 
may  be  real  or  virtual,  and  on  the  principal  axis  or  on  a 
secondary  axis.     The  distance  from  the  optical  centre  of  a 
lens  to  the  principal  focus  is  called  the  focal  length  of  the 
lens.     The  greater  the  curvature  of  a  lens,  and  the  greater 
the  refractive  power  of  the  material  of  which  it  is  com- 
posed, the  shorter  the  focal  length  of  the  lens. 

295.  Divergent  Rays  with  Lenses. — (i.)    Figure  234  repre- 
sents the  case  of  divergent  rays  with  a  convex  lens  when  the 


234 


NATURAL    PHILOSOPHY. 


point  of  divergence  is  on  the  principal  axis  of  the  lens  and 
at  the  focal  length  of  the  lens.  This  is  the  reverse  of  the  case 
shown  in  Figure  229.  Hence, 
according  to  the  principle  of  the 
reversibility  of  the  paths  of  rays 
of  light  through  a  medium,  the 
rays  would  become  parallel  on 
emerging  from  the  lens.  In  the 
case  of  rays  diverging  from  the  focal  length  of  a  convex  lens, 
the  rays  always  become  parallel  to  the  axis  on  which  the  point 
of  divergence  lies. 

(2.)  Figures  235  and  236  represent  the  case  of  divergent  rays 
with  a  convex  lens  when  the  point  of  divergence  is  beyond  the 
focal  length.  In  Figure  235  the  point  of  divergence  is  on  the 

Fig. 


principal  axis,  and  in  Figure  235  on  a  secondary  axis.  Since 
the  rays,  on  meeting  the  lens,  are  less  divergent  than  in  the  pre- 
ceding case,  they  become  convergent  on  emerging  from  the 
lens,  and  have  a  real  focus  at  f. 

The  nearer  the  point  D  to  /%  the  more  nearly  parallel  the 
rays  emerging  from  the  lens,  and  the  farther  the  focus  from  the 
lens. 

Divergent  rays  with  a  convex  lens,  the  point  of  diver- 
gence being  beyond  the  focal  length  of  the  lens,  become 
convergent  on  emerging  from  the  lens,  and  have  a  real 
focus  on  the  opposite  side  of  the  lens  to  that  on  which  the 
rays  enter,  on  the  same  axis  as  the  point  of  divergence,  and 


NATURAL    PHILOSOPHY.  235 

at  a  distance  greater  than  the  focal  length,  and  increasing 
with  the  nearness  of  the  point  of  divergence  to  the  princi- 
pal focus  of  the  lens. 

(3.)   Figures  237  and  238  represent  the  case  of  divergent 
rays  with  a  convex  lens  when  the  point  of  divergence  is  within 
Fig.  237.  Fig.  238. 


the  focal  length  of  the  lens.  The  rays  are  more  divergent  on 
meeting  the  lens  than  in  the  first  case.  Hence  they  become 
only  less  divergent  on  emerging  from  the  lens,  and  have  a  vir- 
tual focus  at/". 

The  nearer  the  point  D  to  f,  the  more  nearly  parallel  the  rays 
on  emerging  from  the  lens,  and  the  more  distant  the  focus  f. 

Divergent  rays  with  a  convex  lens,  when  the  point  of 
divergence  is  within  the  focal  length  of  the  lens,  become 
less  divergent  on  emerging  from  the  lens,  and  have  a  vir- 
tual focus  on  the  same  side  of  the  lens  as  that  on  which 
the  rays  enter,  on  the  same  axis  as  the  point  of  divergence, 
and  at  a  distance  from  the  lens  greater  than  that  of  the 
point  of  divergence,  and  increasing  with  the  nearness  of 
the  point  of  divergence  to  the  principal  focus. 

(4.)  Figure  239  represents  the  case  of  divergent  rays 
with  a  concave  lens.  The  rays  be- 
come more  divergent,  and  have  a 
virtual  focus,  on  the  same  side  of  the 
lens  as  that  on  which  the  rays  enter, 
on  the  same  axis  as  the  point  of  di- 
vergence, and  nearer  the  lens. 

296.  Convergent  Rays  -with  Lenses.  —  (i.)  Figure  240  rep- 
resents the  case  of  convergent  rays  with  a  concave  lens,  with 
the  point  of  convergence  (C)  at  the  focal  length.  This  is  the 


236 


NATURAL    PHILOSOPHY. 


Fig.  240. 


reverse  of  the  case  represented 
in  Figure  232.  The  rays,  on 
emerging  from  the  lens,  be- 
come parallel  with  the  axis  on 
which  the  point  of  convergence 
lies. 

(2.)   Figures  241  and  242   represent   the  case  of   con- 
vergent rays  with  a  concave  lens  when  the  point  of  con- 
Fig.  241. 


vergence  is  beyond  the  focal  length  of  the  lens.  The 
rays,  being  less  convergent  on  meeting  the  lens  than  in  the 
previous  case,  become  divergent  on  emerging  from  the 

Fig.  242. 


lens,  have  a  virtual  focus  on  the  same  side  of  the  lens  as 
that  on  which  the  rays  enter,  on  the  same  axis  as  the 
point  of  convergence,  and  farther  from  the  lens  than  the 
focal  length  of  the  lens.  The  nearer  the  point  of  con- 
vergence to  the  principal  focus  of  the  lens,  the  more  dis- 
tant the  focus  of  the  rays,  because  the  more  nearly  parallel 
the  rays  on  emerging  from  the  lens. 

(3.)   Figure  243  represents  the  case  of  convergent  rays  with  a 
concave  lens  when  the  point  of  convergence  is  within  the  fogal 


NATURAL  PHILOSOPHY.  237 

length  of  the  lens.     The  rays  are  more  convergent  on  meet- 
ing  the   lens  than  in  the  first  case.     Hence  they  become  only 
less    convergent     on     emerging    from 
the  lens,  and  have  a  real  focus,  on  the 
opposite  side  of  the    lens   to   that   on 
which  they  enter,  on  the  same  axis  as 
the  point  of  convergence,  and  at  a  dis- 
tance from  the  lens  greater  than  that  of 
the  point  of  convergence. 

The  nearer  the  point  of  convergence  to  the  principal  focus  of 
a  lens,  the  more  distant  the  focus,  because  the  more  nearly  par- 
allel the  rays  on  emerging  from  the  lens. 

(4.)  Figure  244  represents  the  case  of  convergent  rays  with 
a  convex  lens.  The  rays  become  Fig.  244. 

more  convergent  on  emerging 
from  the  lens,  and  have  a  real 
focus,  on  the  opposite  side  of  the 
lens  to  that  on  which  the  rays 
enter,  on  the  same  axis  as  the 
point  of  convergence,  and  nearer  than  the  point  of  convergence 
to  the  lens. 

297.  Images  formed  by  Lenses.  —  Rays  are  diverging  from 
every  point  on  the  surface  of  an  object  ;  that  is  to  say, 
every  point  on  the  surface  of  an  object  is  a  point  of  di- 
vergence. The  focus  of  a  point  is  a  copy  or  image  of  that 
point,  and  the  foci  of  all  the  points  on  the  surface  of  an 
object  form  an  image  of  the  object. 

To  find  the  image  of  an  object,  it  is  necessary  to  find 
only  the  foci  of  its  extremities.  To  find  these  foci,  we  have 
only  to  draw  axes  through  the  extremities  of  the  object, 
and  locate  the  foci  on  these  axes,  according  to  the  case  of 
divergent  rays  under  which  they  come. 

(i.)  Figure  245  represents  the  Fie  2-»s- 

case  of  an  object  A  B  beyond 
the  focal  length  of  the  lens. 
The  image  ab  is  real,  because 
made  up  of  real  foci ;  inverted, 


238  NATURAL    PHILOSOPHY. 

because  the  axes  cross  between  the  image  and  the  ob- 
ject ;  and  in  this  case  larger  than  the  object,  because 
farther  than  the  object  from  the  lens.  Were  the  object 
distant,  the  image  would  be  nearer  than  the  object  to  the 
lens,  and  consequently  smaller  than  the  object.  The  nearer 
the  object  to  the  principal  focus  of  the  lens,  the  more  dis- 
tant and  the  larger  the  image. 

(2.)    Figure  246  represents  the  case  of  an  object  A  B 
within  the  focal  length  of  a  convex  lens.     The  image  a  b 
is  virtual,  because  made   up  of  virtual 
Fig.  246.  foc;  ^    erect,    because   the   axes   do   not 

cross  between  the  image  and  the  ob- 
ject ;  and  larger  than  the  object,  be- 
cause farther  from  the  lens.  The  nearer 
the  object  to  the  principal  focus  of  the 
lens,  the  more  distant  and  the  larger  the 
image. 

(3.)  Figure  247  represents  the  case  of  an  object  AB 
with  a  concave  lens.  The  image  a  b  is  virtual,  because 
made  up  of  virtual  foci;  erect,  be- 
cause the  axes  do  not  cross  be- 
tween the  image  and  the  object ; 
and  smaller  than  the  object,  because 
nearer  the  lens. 

Virtual  images  can  be  seen  only 
by  looking  through  the  lens  at  the  object. 

298.    To  determine  the  Position  of  the  Image.  —  The  posi- 
F'g-  2-*8-  tion  of  an  image  may  be 

determined  by  the  follow- 
ing construction.  Take 
any  point  A  of  the  object 
A  B  (Figure  248),  and 
draw  an  axis  A  O  through 
it.  Draw  A  A'  parallel  to 
the  principal  axis.  Draw  a  line  from  A  through  the  principal 


NATURAL    PHILOSOPHY. 


239 


focus  F,  and  prolong  it  till  it  meet  the  axis  A  0.  The  point  a, 
at  which  the  lines  meet,  will  be  the  position  of  the  focus  of  A. 
By  a  similar  construction  we  may  locate  the  focus  of  B.  Figure 
249  shows  the  application  of  this  construction  to  the  case  of  a 
virtual  image  formed  by  a  convex  lens.  Figure  250  shows  the 
application  of  the  same  construction  to  the  case  of  a  virtual 
image  formed  by  a  concave  lens. 

Fig.  249. 


299.  Magnifying  Power  of  Lenses.  —  (i.)  When  an  object 
is  40  or  50  feet  distant,  the  rays  from  it  which  fall  upon  a 
small  lens  are  sensibly  parallel,  and  are  brought  to  a  focus 
nearly  at  its  focal  length.  The  image  of  a  distant  object 
is,  therefore,  formed  nearly  at  the  focal  length  of  a  lens. 
Hence,  the  longer  the  focal  length  of  a  lens,  the  larger  the 
image  it  will  form  of  a  distant  object. 

(2.)  When  we  can  place  the  object  as  near  the  princi- 
pal focus  of  the  lens  as  we  please,  the  shorter  the  focal 
length  of  a  lens,  the  larger  the  image  it  will  form.  This  is 
readily  seen  from  Figure  251.  The  two  lenses  i  and  2  are 
represented  as  in  the  same  position.  F  is  the  principal 
focus  of  the  first  lens,  and  F"  that  of  the  second  lens. 
A  B  represents  the  same  objects  placed  near  the  principal 


246 


NATURAL  PHILOSOPHY. 


focus  of  each  lens,  so  that  each  will  form  an  image  of  it  at 
the  same  distance  on  the  other  side  of  the  lenses.     The 


image  a'  V,  formed  by  the  first  lens,  is  seen  to  be  smaller 
than  the  image  a"l>",  formed  by  the  second  lens. 

300.  Spherical  Aberration.  —  The  rays  which  pass  through 
an  ordinary  lens  near  the  margin  are  brought  to  a  focus  a 

Fig.  252.  little    nearer   the    lens   than    those 

which  pass  through  the  lens  near 
the  centre,  as  is  shown  in  Fig- 
ure 252.  This  action  of  the  lens 
is  called  spherical  aberration.  It 
causes  the  image  to  appear  blurred. 
It  can  be  obviated  only  by  grinding  the  lens  to  a  special 
form,  which  can  be  exactly  ascertained  only  by  trial. 

301.  Chromatic  Aberration.  —  An    ordinary    lens    not 
only  refracts,  but  also  disperses  the  rays  of  light.     The 

effect  of  this  dispersion  is  shown 
in  Figure  253.  The  violet  rays, 
which  are  most  refrangible,  are 
brought  to  a  focus  at  i,  while  the 
red  rays,  which  are  least  refran- 
gible, are  brought  to  Fig.  254. 
a  focus  at  2.  The  other  rays  are  brought  to  a 
focus  between  these  points.  This  action  of  the 
lens  is  called  chromatic  aberration.  It  causes 
the  image  to  be  fringed  with  colors.  It  can  be 
overcome  by  combining  a  convex  lens  of  crown 
glass  with  a  concave  lens  of  flint  glass,  which 


Fig.  253. 


NATURAL    PHILOSOPHY.  24! 

has  an  equal  dispersive  power,  but  a  smaller  refractive 
power.  Such  a  combination  of  lenses  is  called  an  achro- 
matic lens.  It  is  shown  in  Figure  254. 

Kit;.  255. 


302.    Concave  Mirrors   correspond  to    Convex   Lenses. — 
Lenses  act  by  refraction,  and   mirrors  by  reflection.     The 

Fig.  256. 


result  of  the  action  of  a  concave  mirror  on  rays  of  light 
is  the  same  as  that  of  a  convex  lens.     A  concave  mirror 

Fig.  257. 


MM^^^.n. , ~-- 

causes   parallel    rays   after   reflection   to   converge    to   a 


242 


NATURAL   PHILOSOPHY. 


principal  focus  (Figure  255) ;  rays  diverging  from  a  point 
beyond  the  principal  focus  to  become  convergent  (Figure 
256)  ;  and  rays  diverging  from  a  point  within  the  principal 
focus  to  become  less  divergent  (Figure  257). 

Fig.  258. 


It  follows  that  concave  mirrors  will  form  the  same  im- 
ages as  a  convex  lens.  The 
image  formed  by  a  concave 
mirror  of  an  object  beyond 
its  focal  length  (Figure  258) 
is  real  and  inverted,  as  in 
the  corresponding  case  of  a 
convex  lens. 

The  image  formed  by  a 
concave  mirror  of  an  object 
placed  within  its  focal  length 
(Figure  259)  is  virtual,  erect, 
and  larger  than  the  object, 
as  in  the  corresponding  case 
with  a  convex  lens'. 

To  avoid    spherical  aber- 
ration, the  reflecting  surface  of  the  concave  mirror  should 


NATURAL   PHILOSOPHY. 


243 


have   a    curvature   as    nearly   that   of    the    parabola    as 
possible. 

The  image  formed  by  a  convex  mirror  is  virtual,  erect,  and 
smaller  than  the  object,  as  in  the  case  of  a  concave  lens. 

F.  OPTICAL  INSTRUMENTS. 

303.  Simple  Microscope.  —  A  simple  microscope  consists  of 
a  convex  lens  mounted  in  any  convenient  way.  The  ob- 
ject to  be  examined  is  placed  a  little  within  its  focal  length, 
and  the  image  seen  on  looking  through  the  lens  is 
virtual,  erect,  and  larger  than  -the  object.  The  shorter 
the  focal  length  of  the  lens,  the  greater  the  magnifying 
power  of  the  microscope.  When  great  magnifying  power 
is  desired,  it  is  better  to  use  two  or  more  convex  lenses 


than  a  single  lens  of  greater  curvature.  The  lenses  are 
combined  so  as  to  act  as  a  single  lens,  and  they  give  a 
larger  and  flatter  field  with  less  spherical  aberration  than  a 
single  lens  of  the  focal  length  of  the  combination. 

304.  Compound  Microscope  and  Celestial  Telescope.  — The 
combination  of  lenses  employed  in  these  two  instruments 
is  shown  in  Figure  260.  AB  is  the  object;  i  is  the  ob- 
jective lens,  2  is  the  eye-piece,  ab\%  the  image  formed  by  the 
objective,  and**'//  is  the  image  formed  by  the  eye-piece. 
The  object  is  beyond  the  focal  length  of  the  objective. 
The  first  image  is  real,  inverted,  and  either  larger  or 
smaller  than  the  object  according  to  the  distance  of  the 
object.  The  rays  which  meet  at  every  point  of  the  first 


244  NATURAL   PHILOSOPHY. 

image  cross  and  diverge  in  front  of  the  image  as  from  an 
object.     The  eye-piece  is  a  simple  microscope  for  examin- 


ing this  image  as  if  it  were  an  object.     The  image  formed 
by  the  eye-piece  is  virtual,  erect  as  compared   with   the 

Fig.  262. first  image,  and  larger  than 

that  image.  It  is  inverted, 
as  compared  with  the  object, 
and  whether  larger  or  smaller 
than  the  object  depends  upon 
the  size  of  the  first  image 
compared  with  that  of  the 
object. 

A  telescope  is  an  instrument 
for  examining  distant  objects. 
With  the  telescope  the  first 
image  is  smaller  than  the 
object,  and  increases  in  size 
with  the  focal  length  of  the 
objective.  Hence  for  pow- 
erful telescopes  the  objec- 
tive is  ground  flat,  so  as  to 
have  as  great  focal  length 
as  possible,  and  made  as 
large  as  possible,  to  admit 


NATURAL   PHILOSOPHY.  245 

the  greatest  possible  amount  of  light.  The  largest  ob- 
jectives now  made  are  26  and  30  inches  in  diameter, 
with  a  focal  length  of  from  30  to  40  feet.  They  are 
made  achromatic. 

A  microscope  is  an  instrument  for  examining  minute  ob- 
jects. The  object,  being  under  our  control,  can  be  placed 
as  near  the  lens-  as  we  please,  and  hence  the  first  image 
will  be  larger  than  the  object,  and  the  less  the  focal  length 
of  the  objective  the  larger  the  image.  Hence,  for  a  pow- 
erful microscope,  the  objective  is  made  of  as  short  a  focal 
length  as  possible,  and  since  it  curves  very  rapidly  it  must 
be  very  small. 

The  objective  and  eye-piece  of  the  telescope  and  micro- 
scope are  mounted  in  a  tube  (Figures  261  and  262).  The 
eye-piece  is  movable,  and  adjusted  so  that  the  final  image 
is  about  10  inches  from  the  eye,  the  point  of  most  distinct 
vision. 

305.  The  Magnifying  Power  of  the  Telescope  and  of  the 
Microscope.  —  The  magnifying  power  of  a  telescope  is  the  ratio 
of  the  apparent  size  of  the  final  image  to  that  of  the  object 
at  its  actual  distance  ;  that  is,  if  the  angle  subtended  by  the 
final  image  is  10  times  that  subtended  by  the  object  at  its 
actual  distance,  the  telescope  is  said  to  magnify  10  diameters. 
Terrestrial  telescopes  on  stands  usually  magnify  from  20  to  60 
diameters.  The  powers  chiefly  used  in  astronomical  observa- 
tion are  from  100  to  500.  The  magnifying  power  of  a  celestial 
telescope  is  approximately  equal  to  the  quotient  of  the  focal 
length  of  the  objective  divided  by  that  of  the  eye-piece. 

The  magnifying  power  of  a  microscope  is  the  ratio  of  the 
apparent  size  of  the  final  image  to  that  of  the  object  at  the  same 
distance ;  that  is,  if  the  angle  subtended  by  the  final  image  is 
50  times  that  which  would  be  subtended  by  the  object  at  the 
same  distance,  the  microscope  is  said  to  magnify  50  diameters. 
The  magnifying  power  of  a  compound  microscope  is  the  product 
of  the  magnifying  powers  of  its  objective  and  eye-piece.  The 
magnifying  power  of  a  compound  microscope  varies  from  50  to 
1500  diameters. 


246 


NATURAL   PHILOSOPHY. 


306.  Terrestrial  Telescope.  —  In  the  celestial  telescope 
objects  are  always  seen  inverted ;  but  this  causes  no  in- 
convenience in  observing  the  heavenly  bodies.  To  make 
terrestrial  objects  appear  erect,  a  second  objective  is  used 


Fig.  263. 


to  invert  the  image  formed  by  the  first  (Figure  263). 
A  B  is  the  object ;  a  b,  the  image  formed  by  the  first  ob- 
jective, which  falls  without  the  focal  length  of  the  second 
objective ;  and  a'  b'.  that  formed  by  the  second  objective. 
Both  images  are  real,  and  the  second  image  is  erect  as 
compared  with  the  object.  One  or  both  of  these  objectives 
may  be  compound. 

307.  The  Opera-Glass.  —  The  objective  of  an  opera-glass 
is  a  convex  lens,  like  that  of  the  ordinary  telescope,  but 
the  eye-piece  is  a  concave  lens.  This  lens  is  placed  so 
that  the  real  image  of  the  objective  would  fall  beyond  it 
and  outside  of  its  principal  focus  (Figures  264  and  265). 


A  B  is  the  object;  i  the  objective,  2  the  eye-piece,  ab  the 
image  that  would  be  formed  by  the  objective  alone,  and 
a'  b'  the  image  formed  by  the  eye-piece.  The  rays  which 
meet  the  eye-piece  from  the  objective  are  converging  to 


NATURAL    PHILOSOPHY. 


247 


points  between  a  and  b.  The  final  image  a' ' fr 'is  virtual, 
erect,  and  larger  than  the  first  image  would  have  been. 
The  two  tubes  of  an  opera-glass  are  exactly  alike.  They 
are  used  because  it  is  less  fatiguing  to  use  both  eyes  than 
only  one.  Each  tube  is  a  Galilean  telescope. 

Fig.  265. 


When  a  convex  and  a  concave  lens  are  arranged  so  that  the 
real  image  of  the  convex  lens  would  fall  beyond  the  concave 
lens,  and  within  its  focal  length,  as  shown  in  Figure  266,  the 
point  of  convergence  being  within  the  focal  length  of  the  con- 
cave lens,  the  image  a  b  that  would  be  formed  by  that  lens 
will  be  real  and  larger  than  the  first  image.  This  arrangement 
of  lenses  is  sometimes  used  for  projecting  images  on  a  screen. 

Fig.  266. 


308.  Reflecting  Telescope.  —  In  reflecting  telescopes,  the 
place  of  an  object-glass  is  supplied  by  a  concave  mirror, 
called  a  speculum,  usually  composed  of  solid  metal.  The 
real  and  inverted  image  which  it  forms  of  distant  objects 


248  NATURAL    PHILOSOPHY. 

is,  in  the  Herschelian  telescope,  viewed  directly  through 
an  eye-piece,  the  back  of  the  observer  being  towards  the 
object  and  his  face  towards  the  speculum  (Figure  267). 

Achromatic  refracting  telescopes  give  much  better  results, 
both  as  legards  light  and  definition,  than  reflectors  of  the  same 
size  or  weight ;  but  it  has  been  found  practicable  to  make 
specula  of  much  larger  size  than  object-glasses.  The  aperture 
of  Lord  Rosse's  largest  telescope  is  six  feet,  whereas  that  of 
the  largest  achromatic  telescopes  yet  made  is  less  than  three 
feet,  and  increase  of  size  involves  increased  thickness  of  glass, 
and  consequent  absorption  of  light. 

Fig.  267. 


The  massiveness  which  is  found  necessary  in  the  speculum 
in  order  to  prevent  flexure  is  a  serious  inconvenience,  as  is  also 
the  necessity  for  frequent  repolishing, — an  operation  of  great 
delicacy,  as  the  slightest  change  in  the  form  of  the  surface  im- 
pairs the  definition  of  the  images.  Both  these  defects  have 
been  to  a  certain  extent  remedied  by  the  introduction  of  glass 
specula,  covered  in  front  with  a  thin  coating  of  silver.  Glass  is 
much  more  easily  worked  than  speculum-metal,  and  is  only  one 
third  as  heavy.  Silver  is  also  much  superior  to  speculum-metal 
in  reflecting  power,  and  when  it  is  tarnished  it  can  be  removed 
and  renewed  without  liability  to  change  of  form  in  the  glass. 

309.  The  Camera  Obscura.  —  The  camera  obscura  is  a 
dark  chamber  having  a  movable  screen  within  it,  and 
a  convex  lens  fitted  into  an  opening  in  front.  This  lens 
forms  a  real  inverted  image  of  the  objects  in  front,  which 
is  received  upon  the  screen.  If  the  objects  in  the  external 


NATURAL   PHILOSOPHY. 


249 


landscape  depicted  are  all  at  distances  many  times  greater 
than  the  focal  length  of  the  lens,  their  images  will  all  be 
formed  at  sensibly  the  same  distance  from  the  lens,  and 
may  be  received  upon  a  screen  placed  Fig.  268. 
at  this  distance.  In  order  to  receive  the 
image  on  a  horizontal  table,  a  lens  of 
the  form  shown  in  Figure  268  is  some- 
times used  at  the  top  of  the  camera.  The 
rays  from  external  objects  are  first  re- 
fracted at  the  convex  surface,  then  totally 
reflected  at  the  back  of  the  lens,  which 
is  plane,  and  finally  emerge  through  the 
bottom  of  the  lens,  which  is  concave,  but 
with  a  larger  radius  of  curvature  than  the 
first  surface.  The  two  refractions  produce  the  effect  of  a 
converging  meniscus.  The  camera  obscura  employed  by 


Fig.  269. 


photographers  (Figure  269)  is  a 
box  MN,  with  a  tube  A  B  in 
front,  containing  an  object-glass 
at  its  extremity.  The  object- 
glass  is  usually  compound,  con- 
sisting of  two  single  lenses  EL; 
an  arrangement  which  is  very 
commonly  adopted  in  optical  in- 
struments, and  which  has  the 
advantage  of  giving  the  same 
effective  focal  length  as  a  sin- 
gle lens  of  smaller  radius  of 
curvature,  while  it  permits  the 
employment  of  a  larger  aper- 
ture, and  consequently  gives 
more  light.  At  G  is  a  slide 
of  ground  glass,  on  which  the  image  of  the  scene  to  be 
depicted  is  thrown,  in  setting  the  instrument.  The  focus- 
ing is  performed  in  the  first  place  by  sliding  the  part  M 


250  NATURAL   PHILOSOPHY. 

of  the  box  in  the  part  JV,  and  finally  by  the  pinion  F,  which 
moves  the  lens.  When  the  image  has  thus  been  rendered 
as  sharp  as  possible,  the  sensitized  plate  is  substituted  for 
the  ground  glass. 

310.  Lantern  for  Projection. — The  lantern  is  now  ex- 
tensively used  by  teachers  and  lecturers  for  projecting 
experiments,  diagrams,  and  views  of  various  kinds  upon 
the  screen.  This  lantern  is  a  kind  of  reversed  camera. 
Some  intense  artificial  light,  as  the  lime  light  or  the  electric 
light,  is  enclosed  in  an  opaque  box.  A  convex  lens,  called 
the  condenser,  fixed  in  an  opening  in  the  front  of  the  box, 
condenses  the  light  upon  the  transparent  picture  or  object 
to  be  projected.  In  front  of  this  object  is  a  tube  contain- 
ing a  combination  of  lenses  exactly  like  those  used  with 
the  camera.  These  form  a  real  inverted  image  of  the  ob- 
ject on  the  distant  screen.  Owing  to  the  distance  of  the 
screen,  the  image  is  many  times  as  large  as  the  object. 

Fig.  270. 


311.  The  Eye.  —  The  human  eye  (Figure  270)  is  a  nearly 
spherical  ball,  capable  of  turning  in  any  direction  in  its  socket. 
Its  outermost  coat  is  thick  and  horny,  and  is  opaque  except  in 
its  anterior  portion.  Its  opaque  portion  H  is  called  the  scle- 


NATURAL   PHILOSOPHY.  251 

rotic  coat,  or  in  common  language  the  white  of  the  eye.  Its 
transparent  portion  A  is  called  the  cornea,  and  has  the  shape  of 
a  very  convex  watch-glass.  Behind  the  cornea  is  a  diaphragm 
D,  of  annular  form,  called  the  iris.  It  is  colored  and  opaque, 
and  the  circular  aperture  C  in  its  centre  is  called  the  pupil.  By 
the  action  of  the  involuntary  muscles  of  the  iris,  this  aperture 
is  enlarged  or  contracted  on  exposure  to  darkness  or  light.  The 
color  of  the  iris  is  what  is  referred  to  when  we  speak  of  the 
color  of  a  person's  eyes.  Behind  the  pupil  is  the  crystalline 
lens  E,  which  has  greater  convexity  at  back  than  in  front.  It  is 
built  up  of  layers  or  shells,  increasing  in  density  inwards.  This 
latter  circumstance  tends  to  diminish  spherical  aberration.  The 
cavity  B  between  the  cornea  and  the  crystalline  is  called  the 
anterior  chamber,  and  is  filled  with  a  watery  liquid  called  the  aque- 
ous humor.  The  much  larger  cavity  Z.,  behind  the  crystalline, 
is  called  the  posterior  chamber,  and  is  filled  with  a  transparent 
jelly  called  the  vitreous  humor,  enclosed  in  a  very  thin  trans- 
parent membrane.  The  posterior  chamber  is  enclosed,  except 
in  front,  by  the  choioid  coat  /,  which  is  saturated  with  an  in- 
tensely black  and  opaque  mucus,  called  the  black  pigment.  The 
choroid  is  lined  except  in  its  anterior  portion,  with  another  mem- 
brane K,  called  the  retina,  which  is  traversed  by  a  ramified  sys- 
tem of  nerve  filaments  diverging  from  the  optic  nerve  M. 

It  is  clear,  from  the  above  description,  that  a  pencil  of  rays 
entering  the  eye  from  an  external  point  will  undergo  a  series  of 
refractions,  first  at  the  anterior  surface  of  the  cornea,  and  after- 
wards in  the  successive  layers  of  the  crystalline  lens,  all  tending 
to  render  them  convergent.  A  real  and  inverted  image  is  thus 
formed  of  any  external  object  to  which  the  eye  is  directed.  If 
this  image  falls  on  the  retina,  the  object  is  seen  ;  and  if  the 
image  thus  formed  on  the  retina  is  sharp  and  sufficiently  lumi- 
nous, the  object  is  seen  distinctly. 

312.  The  Adjustment  of  the  Eye.  —  As  the  distance  of  an 
image  from  a  lens  varies  with  the  distance  of  the  object,  it  would 
be  possible  to  see  objects  distinctly  at  only  one  particular  dis- 
tance, were  there  not  special  means  of  adjustment  in  the  eye. 
Persons  whose  sight  is  not  defective  can  see  objects  in  good 
definition  at  all  distances  beyond  a  certain  limit.  When  we 
wish  to  examine  the  minute  details  of  an  object  to  the  greatest 


252  NATURAL    PHILOSOPHY. 

advantage,  we  hold  it  at  a  particular  distance,  which  varies  in 
different  individuals,  and  averages  about  eight  inches.  As  we 
move  it  farther  away,  we  experience  rather  more  ease  in  looking 
at  it,  though  the  diminution  of  its  apparent  size  renders  its 
minuter  features  less  visible.  On  the  other  hand,  when  we 
bring  it  nearer  to  the  eye  than  the  distance  which  gives  the  best 
view,  we  cannot  see  it  without  more  or  less  effort ;  and  when  we 
have  brought  it  nearer  than  a  certain  lower  limit  (averaging 
about  six  inches)  we  find  distinct  vision  no  longer  possible.  In 
looking  at  very  distant  objects,  if  our  vision  is  not  defective 
we  have  very  little  sense  of  effort.  These  phenomena  are  in 
accordance  with  the  theory  of  lenses,  which  shows  that  when 
the  distance  of  an  object  is  a  large  multiple  of  the  focal  length 
of  the  lens,  any  further  increase,  even  up  to  infinity,  scarcely 
alters  the  distance  of  the  image  ;  but  that,  when  the  object  is 
comparatively  near,  the  effect  of  any  change  of  its  distance  is 
considerable.  There  has  been  much  discussion  among  physiol- 
ogists as  to  the  precise  nature  of  the  changes  by  which  we  adapt 
our  eyes  to  distinct  vision  at  different  distances.  Such  adapta- 
tion might  consist  either  in  a  change  of  focal  length  or  in  a 
change  of  distance  of  the  retina.  Observations  in  which  the 
eye  of  the  patient  is  made  to  serve  as  a  mirror,  giving  images  by 
reflection  at  the  front  of  the  cornea,  and  at 
the  front  and  back  of  the  crystalline,  have 
shown  that  the  convexity  of  the  front  of  the 
crystalline  is  materially  changed  as  the 
patient  adapts  his  eye  to  near  or  remote 
vision,  the  convexity  being  greatest  for  near 
vision.  This  increase  of  convexity  corre- 
sponds to  a  shortening  of  focal  length,  and 
is  thus  consistent  with  theory. 

313.  The  Structure  of  the  Retina.  —  Fig- 
ure 271  represents  a  portion  of  the  retina 
highly  magnified,  since  the  whole  thickness 
of  this  membrane  does  not  exceed  the  ^ 
of  an  inch.  The  inner  side  a,  which  is  in 
contact  with  the  vitreous  humor,  is  lined  with 
what  is  called  the  limiting  membrane.  Ex- 
ternally and  next  to  the  choroid  coat  it  con- 


NATURAL    PHILOSOPHY.  253 

sists  of  a  great  number  of  minute  rod-like  and  conical  bodies, 
e,  arranged  side  by  side.  This  is  the  layer  of  rods  and  cones, 
and  occupies  a  quarter  of  the  whole  thickness  of  the  retina. 
From  the  inner  ends  of  the  rods  and  cones  very  delicate  radial 
fibres  spread  out  to  the  limiting  membrane  ;  d  and  c  are  layers 
of  granules.  The  fibres  of  the  optic  nerve  are  all  spread  out 
between  b  and  a.  At  the  entrance  of  the  optic  nerve  the  nerve 
fibres  predominate,  and  the  rods  and  cones  are  wanting.  Ex- 
actly at  the  centre  of  the  back  of  the  eye  there  is  a  slight  cir- 
cular depression  of  a  yellowish  hue,  called  the  macula  lutea,  or 
yellow  spot.  In  this  spot  the  cones  are  abundant  without  the 
rods  and  nerve  fibres. 

314.  The  Action  of  Light  on  the  Optic  Nerve.  —  The  distri- 
bution of  the  nerve  fibres  over  the  front  surface  of  the  retina 
would  seem  to  indicate  that  they  are  directly  acted  upon  by  the 
light ;  but  this  is  not  the  case.  The  fibres  of  the  optic  nerve 
are  in  themselves  as  blind  as  any  other  part  of  the  body.  To 
prove  this  we  have  only  to  close  the  left  eye  and  with  the  right 
look  steadily  at  the  cross  on  this  page,  holding  the  book  ten  or 
twelve  inches  from  the  eye.  The  black  dot  will  be  seen  quite 

Fig.  273. 


plainly  as  well  as  the  cross.  Now  move  the  book  slowly  towards 
the  eye,  which  should  be  kept  fixed  on  the  cross.  At  a  certain 
distance  the  dot  will  suddenly  disappear ;  but  on  bringing  the 
book  still  nearer  it  will  come  into  view  again.  Now  it  is  found 
upon  examination  that  when  the  dot  disappears  its  image  falls 
exactly  upon  the  point  where  the  optic  nerve  enters  the  eye,  and 
where  there  are  no  rods  and  cones,  but  merely  nerve  fibres. 
Again,  the  yellow  spot  is  the  most  sensitive  part  of  the  retina, 
though  it  contains  no  nerve  fibres. 

It  would  appear,  then,  that  the  fibres  of  the  optic  nerve  are 
not  directly  affected  by  the  vibrations  of  the  ether,  but  only 
through  the  rods  and  cones. 

315.  The  Duration  of  the  Impression  on  the  Retina.  —  The 
impression  made  by  light  on  the  retina  does  not  cease  the  in- 
stant the  light  is  removed,  but  lasts  about  an  eighth  of  a  second. 
If  luminous  impressions  are  separated  by  a  less  interval,  they 


254  NATURAL   PHILOSOPHY. 

appear  continuous.  Thus,  if  a  stick  with  a  spark  of  fire  at  the 
end  is  whirled  round  rapidly,  it  gives  the  impression  of  a  circle 
of  light.  The  spokes  of  a  carriage  wheel  in  rapid  motion  can- 
not be  distinguished. 

The  optical  toy  called  the  thaumatrope,  or  zoetrope,  illustrates 
the  same  principle.     It  consists  (Figure  273)  of  a  cylindrical 
Fig.  273.  paper  box  made  to  rotate  on  an  upright 

axis.  Near  the  top  of  the  box  is  a  row 
of  slits.  The  successive  positions  which 
a  moving  body  assumes  are  represented 
in  order  upon  a  strip  of  paper ;  and  this 
paper  is  put  within  the  box,  which  is  then 
whirled  round  rapidly.  If  we  look  at  the 
figures  through  the  slits,  the  succes- 
sive positions  come  before  the  eye  one 
after  another,  and  the  impression  of  each  lasts  till  the  next 
arrives,  so  that  they  all  blend  into  one,  and  the  object  appears  to 
be  really  going  through  the  evolutions  represented. 

316.  Irradiation. — When  a  white  or  very  bright  object  is 
seen  against  a  black  ground  it  appears  larger  than  it  really  is, 
while  a  black  object  on  a  white  ground  appears  smaller  than  it 
really  is.  The  two  circles  given  in  Figure  274  illustrate  this. 

Fig.  274- 


The  black  one  and  the  white  one  have  just  the  same  diameter. 
This  effect  is  called  irradiation.  It  arises  from  the  fact  that 
the  impression  produced  by  a  bright  object  on  the  retina  ex- 
tends beyond  the  outline  of  the  image.  It  bears  the  same  rela- 
tion to  the  space  occupied  by  the  image  as  the  duration  of  the 
impression  does  to  the  duration  of  the  image. 

3 1 7.    The  Optical  Axis  and  the  Visual  A  ngle.  —  A  line  drawn 


NATURAL   PHILOSOPHY.  255 

from  the  centre  of  the  yellow  spot  through  the  centre  of  the  pu- 
pil is  called  the  optical  axis.  When  we  look  at  any  object  we 
must  turn  the  eye  so  as  to  direct  this  axis  towards  it.  This  ena- 
bles us  to  appreciate  the  direction  of  the  object. 

We  have  seen  that  the  image  of  a  candle  or  other  object, 
formed  by  a  convex  lens,  is  contained  between  lines  drawn  from 
the  extremities  of  the  object  through  the  centre  of  the  lens. 
In  the  same  way  the  image  of  an  object  on  the  retina  is  con- 
tained between  lines  drawn  from  the  extremities  of  the  object 
through  the  centre  of  the  crystalline  lens.  The  angle  contained 
between  lines  thus  drawn  is  called  the  visual  angle  of  the  ob- 
ject, and  of  course  measures  the  length  of  the  image  on  the 
retina.  All  objects  which  have  the  same  visual  angle  form 
images  of  the  same  length  on  the  retina. 

318.  How  we  estimate  the  Size  of  a  Body.  —  The  visual  angle 
evidently  gives  us  no  information  as  to  the  real  size  of  a  body  ; 
for  we  see  from  Figure  275  that  the  visual  angle  of  a  body  dimin- 

Fig.  275. 


ishes  as  its  distance  increases,  and  also  that  bodies  at  different 
distances  may  have  the  same  visual  angle,  though  they  are 
not  of  the  same  size.  Thus,  A  B  and  A'B'  are  the  same  ob- 
ject ;  but  A' B' ,  which  is  farther  off,  has  the  smaller  visual  angle. 
Again,  CD  and  A'B'  have  the  same  visual  angle,  but  A'B1  is 
the  larger.  We  must,  then,  know  the  distance  of  a  body,  in  order 
to  estimate  its  size  ;  but  when  we  know  this  distance,  we  esti- 
mate its  size  instinctively.  Thus,  a  chair  at  the  farthest  end  of- 
the  room  has  a  visual  angle  only  half  as  large  as  a  chair  at  half 
the  distance,  yet  we  cannot  make  it  seem  smaller  if  we  try.  If 
we  are  in  any  way  deceived  as  to  the  distance  of  an  object,  we 
are  also  deceived  as  to  its  size. 

319.  How  we  estimate  the  Distance  of  an  Object.  —  If  we 
refer  to  Figure  276,  we  see  that  when  the  eyes  are  directed  to 
a  distant  object,  as  C,  they  are  turned  inward  but  slightly,  while 


256  NATURAL   PHILOSOPHY. 

they  are  turned  inward  considerably  when  directed  to  the  nearer 
object  D.  The  muscular  effort  we  have  to  make  in  thus  turning 
the  eyes  inward  so  as  to  direct  them  upon  an  object  is  one  of  the 
best  methods  we  have  of  estimating  its  distance. 

Again,  we  have- seen  that  we  have  to  adjust  the  eye  for  differ- 
ent distances,  and  the  effort  we  have  to  make  in  this  adjustment 
helps  us  to  judge  of  the  distance. 

We  also  judge  of  the  distance  of  an  object  from  the  distinct- 
ness with  which  we  see  it.  The  more  obscure  it  is,  the  more  dis- 
tant it  seems.  It  is  for  this  reason  that  objects  seen  in  a  fog 
sometimes  appear  enormously  large.  They  appear  indistinct, 
and  we  cannot  rid  ourselves  of  the  impression  that  they  are  far 
off;  and  hence  they  seem  large,  though  they  may  really  be  small 
and  near  us. 

Fig.  276. 


The  celebrated  "  Spectre  of  the  Brocken,"  seen  among  the 
Hartz  Mountains,  is  a  good  illustration  of  the  effect  of  indistinct- 
ness upon  the  apparent  size  of  an  object.  On  a  certain  ridge, 
just  at  sunrise,  a  gigantic  figure  of  a  man  had  often  been  seen 
walking,  and  extraordinary  stories  were  told  of  him.  About  the 
year  1800  a  French  philosopher  and  a  friend  went  to  watch  the 
spectre.  For  many  mornings  they  looked  for  it  in  vain.  At  last, 
•however,  the  monster  was  seen,  but  he  was  not  alone.  He  had 
a  companion,  and,  singularly  enough,  the  pair  aped  all  the  mo- 
tions and  attitudes  of  the  two  observers.  In  fact,  the  spectres 
were  merely  the,  shadows  of  the  observers  upon  the  morning  fog, 
which  hovered  over  the  valley  between  the  ridges  ;  and  because 
the  shadows,  though  near,  were  very  faint,  the  figures  seemed 
to  be  distant,  and  like  gigantic  men  walking  on  the  opposite 
ridge. 


NATURAL    PHILOSOPHY.  257 

When  we  know  the  real  size  of  an  object,  we  judge  of  its  dis- 
tance from  the  visual  angle  ;  but  we  judge  of  the  distance  of 
unknown  objects  mainly  by  comparing  it  with  the  distance  of 
known  objects. 

This  is  one  reason  why  the  moon  appears  larger  near  the  hori- 
zon than  overhead,  though  she  is  really  nearer  in  the  latter  case. 
When  she  is  on  the  horizon,  we  see  that  she  is  beyond  all  the 
objects  on  the  earth  in  that  direction,  and  therefore  she  seems 
farther  off  than  when  overhead,  where  there  are  no  intervening 
objects  to  help  us  to  judge  of  the  distance. 

320.  Why  Bodies  near  us  appear  Solid.  —  Hold  any  solid 
object,  as  a  book,  about  a  foot  from  the  eyes,  and  look  at  it  first 
with  one  eye,  and  then  with  the  other.  It  will  be  seen  that  the 
two  images  of  the  object  are  not  exactly  alike.  With  the  right 
eye  we  can  see  a  little  more  of  the  right  side  of  the  object,  and 
with  the  left  eye  a  little  more  of  its  left  side.  It  seems  to  be  the 
blending  of  these  two  pictures  which  causes  objects  to  appear 
solid. 

The  principle  just  stated  explains  the  action  of  the  stereo- 
scope. Two  photographs  of  an  ob-  Fi 
ject  are  taken  from  slightly  different 
points  of  view,  so  as  to  obtain  pictures 
like  those  formed  in  the  two  eyes. 
These  photographs  are  placed  before 
the  eyes  in  such  a  manner  that  each 
eye  sees  only  one,  but  both  are 
seen  in  the  same  position.  This  is 
effected  by  the  arrangement  shown 
in  Figure  277.  The  pictures  are 
placed  at  A  and  B.  The  rays  of 
light  from  them  fall  upon  the  lenses 
m  and  «,  and  in  passing  through  them 
are  bent  so  that  they  enter  the  eye  as 
if  they  came  from  the  direction  C. 
The  lenses  are  portions  of  a  double- 
convex  lens,  arranged  as  shown  in  the 
figure. 

321.  Near-sighted  and  Far-sighted  Eyes.  —  To  see  an  object 
distinctly,  a  clear  image  of  it  must  be  formed  on  the  retina.  It 


258  NATURAL    PHILOSOPHY. 

has  been  seen  that  the  eye  has  the  power  of  adjusting  itself  so 
as  to  form  distinct  images  of  objects  at  different  distances. 
When,  however,  an  object  is  brought  quite  near  the  eye,  it  be- 
comes indistinct,  showing  that  there  is  a  limit  to  this  power  of 
adjustment.  The  rays  are  now  so  divergent  that  the  lens  cannot 
bring  them  to  a  focus  on  the  retina.  The  nearest  point  at  which 
a  distinct  image  is  formed  upon  the  retina  is  called  the  near  point 
of  vision,  and  the  greatest  distance  at  which  such  an  image  is 
formed  is  called  the  far  point.  In  perfectly  formed  eyes  the  near 
point  is  about  3^  inches  from  the  eye,  and  the  far  point  is  infi- 
nitely distant.  In  such  eyes  parallel  rays  are  brought  to  a  focus 
exactly  at  the  retina  when  the  eye  is  at  rest,  that  is,  when  the 
crystalline  lens  is  of  its  natural  convexity.  The  pupil  of  the 
eye  is  so  small  that  the  rays  which  fall  upon  it  from  objects  18  or 

Fig.  278. 


20  inches  distant  diverge  so  little  that  they  may  be  regarded  as 
parallel.  The  distance  of  the  near  and  far  points,  however,  is 
not  the  same  for  all  eyes.  In  some  cases  the  near  point  is  con- 
siderably less  than  3^  inches  from  the  eye,  while  the  far  point 
is  only  8  or  10  inches.  In  other  cases  the  near  point  is  12 
inches  from  the  eye,  and  the  far  point  infinitely  distant.  The 
former  are  called  near-sighted  eyes  ;  the  latter,  far-sighted 
ones. 

It  was  once  thought  that  near-sightedness  was  due  to  the  too 
great  convexity  of  the  cornea  or  the  crystalline  lens,  or  of  both, 
and  far-sightedness  to  the  too  slight  convexity  of  the  same.  But 
actual  measurement  has  shown  that  their  real  cause  lies  in  the 
shape  of  the  eyeball,  which  in  far-sighted  people  is  flattened, 
and  in  near-sighted  people  elongated,  in  the  direction  of  the  axis. 
In  Figure  278  the  curve  N  shows  the  form  of  the  normal  or 


NATURAL    PHILOSOPHY.  259 

perfect  eye,  N'  of  the  far-sighted  eye,  and  N"  of  the  near- 
sighted eye.  In  this  figure  the  eye  is  represented  as  at  rest,  and 
we  see  that  the  parallel  rays  A  and  A  are  brought  to  a  focus  on 
the  retina  of  the  normal  eye,  while  only  the  convergent  rays 
A1  and  A'  are  brought  to*  a  focus  on  the  retina  of  the  far-sighted 
eye,  and  only  the  divergent  rays  A"  on  the  retina  of  the  near- 
sighted eye. 

A",  then,  is  the  far  point  for  the  near-sighted  eye,  since  the 
lens  has  now  its  least  convexity  ;  and  this  point  must  be  within 
1 8  or  20  inches,  since  the  rays  from  an  object  at  a  greater  dis- 
tance are  virtually  parallel,  and  cannot  be  brought  to  a  focus  on 
the  retina.  The  near  point  must  be  less  than  for  the  normal 
eye,  since  the  retina  is  farther  from  the  lens,  and  therefore  rays 
of  greater  divergence  can  be  brought  to  a  focus  upon  it.  In 
the  far-sighted  eye  the  retina  is  nearer  the  lens  than  in  the  nor- 
mal eye  :  hence  the  near  point  must  be  farther  away.  While, 
then,  the  normal  eye  sees  distant  objects  distinctly  without  ad- 
justment, the  far-sighted  eye  must  adjust  itself  to  see  such 
objects. 

The  defect  of  far-sighted  eyes  can  be  in  a  great  measure  reme- 
died by  wearing  convex  glasses,  which  help  to  bring  the  rays  to 
a  focus  on  the  retina,  and  thus  diminish  the  distance  of  the  near 
point.  The  defect  of  near-sighted  eyes  can  be  remedied  by  the 
use  of  concave  glasses,  which  render  parallel  rays  divergent,  and 
thus  increase  the  distance  of  the  far  point. 

322.  Old  Eyes.  — As  the  eye  grows  old  it  loses  its  power  of 
adjustment,  the  crystalline  lens  becoming  less  elastic  ;  hence  old 
eyes  can  see  distinctly  only  distant  objects.  This,  however, 
is  a  very  different  thing  from  far-sightedness.  In  the  far-sighted 
eye  there  is  no  lack  of  power  to  change  the  convexity  of  the 
lens  ;  but  this  power  becomes  useless  because  of  the  distance  of 
the  retina. 

This  defect  of  vision,  caused  by  age,  can  be  remedied  by  the 
use  of  convex  glasses. 


260  NATURAL    PHILOSOPHY. 

G.   COLOR. 

/.    THEORY  OF  COLOR. 

323.  The  Three  Fundamental  Qualities  of  Color.  —  The 
three  fundamental  properties  upon  which  all  the  varied 
characteristics  of  color  depend  are  hue,  purity,  and  brig/it- 
ness. 

The  hue  of  color  depends  upon  the  length  of  the  lumi- 
nous waves,  and  corresponds  to  pitch  in  sound.  In  the 
spectrum  of  an  incandescent  solid  we  have  all  possible 
hues  from  the  red  through  the  green  to  the  violet.  Names 
have  been  given  to  only  a  few  of  the  more  prominent  of 
these  innumerable  hues.  These  prismatic  hues  are  simple. 
Other  hues,  as  for  instance  the  purples,  are  compound ; 
that  is  to  say,  they  are  produced  by  the  mingling  of  two  or 
more  sets  of  wave-lengths. 

By  the  purity  of  a  color  or  hue  we  mean  its  freedom 
from  admixture  with  white  light.  Most  natural  and  artifi- 
cial colors  are  found,  on  analysis  by  the  spectroscope,  to 
contain  a  greater  or  less  proportion  of  white  light  blended 
with  their  fundamental  hue.  The  presence  of  the  white 
light  gives  the  hue  a  certain  tint  which  varies  with  the 
amount  of  the  light  present.  The  more  white  light  present, 
the  paler  the  color.  By  the  brightness  of  a  color  we  mean 
the  amount  of  light  in  it.  If  one  colored  surface  diffuses 
twice  as  much  light  as  another,  its  color  is  said  to  be  twice 
as  bright.  When  a  color  is  at  once  pure  and  bright,  it  is 
said  to  be  intense  or  saturated, 

324.  The  Ideal  Color-Disc.  —  Every  possible  hue  of  color 
would  be  represented  on  a  disc  the  color  of  which  changed 
by  insensible  gradation  from  the  red  through  the  green  to 
the  violet,  and  then  around  through  the  purple  to  the  red 
again.     The  series  of  hues  from  the  red  through  the  green 
to  the  violet  would  be  those  of  the  spectrum,  while  the 
complementary  series  of  hues  from  the  violet  through  the 


NATURAL    PHILOSOPHY.  261 

purple  to  the  red  have  no  representative  among  the  pris- 
matic colors.  As  such  a  disc  can  have  only  an  ideal  exist- 
ence it  is  called  the  ideal  color-disc. 

325.  The  Color  Chart.  —  If  the  ideal  color-disc  were 
divided  into  ten  equal  sectors,  and  each  sector  colored 
with  its  mean  hue  (the  hue  that  would  result  from  the 
blending  of  all  the  hues  of  the  sec-  Fig.  279. 

tor),  there  would  be  obtained  the 
ten  following  colors :  red,  orange, 
yellow,  yellowish  green,  green,  bluish 
green,  turquoise  blue,  ultramarine, 
violet,  and  purple.  The  position  of 
these  colors  on  the  disc  is  shown 
in  Figure  279.  The  disc  thus  di- 
vided and  colored  is  called  the 
color  chart. 

The  colors  of  opposite  sectors  are  complementary  colors, 
that  is,  colors  that  would  produce  white  when  blended. 
We  thus  obtain  the  five  prominent  pairs  of  complementary 
colors,  as  follows :  — 

Red  and  bluish  green, 
Orange  and  turquoise  blue, 
Yellow  and  ultramarine, 
Yellowish  green  and  violet, 
Green  and  purple. 

Had  the  disc  been  divided  into  20  equal  sectors,  and  each 
sector  colored  as  above,  there  would  have  been  produced 
10  pairs  of  complementary  colors  ;  if  into  40  equal  sectors, 
20  pairs  of  complementary  colors  ;  and  so  on.  In  fact, 
were  any  diameter  drawn  through  the  ideal  color-disc,  the 
colors  on  the  disc  at  the  opposite  ends  of  the  diameter 
would  be  complementary  colors.  Comparatively  few  of 
the  hues  on  the  ideal  color-disc  have  ever  been  named. 
In  the  case  of  the  color  chart  the  change  in  color  in 


262 


NATURAL    PHILOSOPHY. 


passing  from  one  sector  to  the  next  is  much  greater  in  the 
neighborhood  of  the  purple  than  in  that  of  the  green. 

326.  The  Color  Scale.  —  In  order  to  have  the  change  in 
color  equal  in  passing  from  one  sector  to  the  next  in  every 
part  of  the  disc,  it  is  necessary  to  make  the  sectors  smaller 

Fig.  280.  in  the  region  of  the  purple  than  in 

that  of  the  green.  In  Figure  280 
the  disc  is  shown  as  divided  into  12 
unequal  sectors  for  equal  change 
in  color  from  sector  to  sector.  Each 
sector  is  colored  as  before.  The 
colors  obtained  are  vermilion,  orange, 
yellow,  yellowish  green,  green,  bluish 
green,  turquoise  blue,  ultramarine, 
bluish  violet,  purplish  violet,  purple,  and  carmine.  This 
arrangement  of  the  disc  is  called  the  -color  scale. 

It  may  be  stated  as  a  general  fact  that  the  colors  which 
are  nearest  together  on  the  scale  form  the  poorest  combina- 
tions, while  those  farthest  apart  form  the  best.  When  the 
colors  are  equally  pure  and  bright,  and  cover  equal  extents 
of  surface,  the  best  possible  combination  that  can  be 
formed  with  any  color  on  the  scale  is  that  formed  with  the 
sixth  color  from  it.  The  two  colors  that  will  under  similar 
conditions  combine  best  with  any  color  are  the  third  colors 
on  each  side  of  that  color  on  the  scale. 

327.  The  Three  Primary  Colors.  —  It  is  found  that  all 
possible  hues  of  color  can  be  obtained  by  mixing  in  various 


Fig 


proportions  the  three  hues,  red,  green, 
and  violet.  Hence  these  three  hues  are 
called  the  three  primary  colors.  In 
Figure  281  these  three  colors  are  ar- 
ranged at  the  three  angles  of  the  trian- 
gle R  G  V.  This  arrangement  is  called 
the  color  triangle. 

By  mixing  the  hues  red  and  green  in 


NATURAE,   PHILOSOPHY. 


various  proportions,  all  the  hues  from  red  to  green  can  be 
obtained.  In  this  admixture  the  proportion  of  the  red 
must  steadily  decrease  and  that  of  the  green  increase  in 
passing  from  the  red  to  the  green.  By  a  similar  admixture 
of  green  and  violet  we  can  obtain  all  the  hues  that  lie 
between  the  green  and  violet ;  and  of  violet  and  red,  all 
the  hues  of  purple  which  lie  between  the  red  and  violet 
opposite  the  green.  The  three  primary  hues  may  be 
blended  by  means  of  the  apparatus  shown  in  Figure  282. 

Fig.  282. 


Three  colored  discs  of  thick  paper  are  employed  with  it. 
One  of  the  discs  must  be  colored  vermilion  red,  another 
emerald  green,  and  the  third  violet  (Hofmann's  violet  B  B). 
Each  disc  has  a  small  hole  in  it  at  the  centre,  and  is  cut 
open  on  one  side  from  the  margin  to  the  centre.  Any  two 
of  the  discs  may  be  combined  by  Fig.  283. 

holding  them   up  with    their  cut 
places  opposite,  and  slipping  one 
of   them   into    the   other  (Figure      V     ~YB.LOW 
283).       By   turning    around    the 


264  NATURAL    PHILOSOPHY. 

discs  thus  combined  the  amount  of  each  disc  exposed  may 
be  varied  at  pleasure. 

Place  the  red  and  green  discs  thus  combined  upon  the 
rotating  disc,  and  put  it  into  rapid  rotation  by  turning  the 
crank.  The  hues  of  the  exposed  portions  of  the  two  discs 
will  be  blended  in  the  eye  by  the  persistence  of  vision,  the 
impression  of  the  color  of  the  exposed  portion  of  each 
disc  remaining  on  the  retina  till  after  the  exposed  portion 
of  the  other  disc  comes  round  into  its  place.  By  changing 
the  proportions  of  the  surfaces  exposed  by  the  discs,  the 
proportions  of  the  two  hues  in  the  admixture  can  be  varied 
at  pleasure.  In  a  similar  way  the  colors  green  and  violet 
and  red  and  violet  may  be  blended  in  various  proportions. 

Fig.  284. 


328.  Difference  between  mixing  Hues  and  mixing  Pig- 
ments.—  Fill  two  glass  tanks  having  parallel  sides,  one  with 
a  solution  of  aniline  yellow,  and  the  other  with  an  ammo- 
niacal  solution  of  sulphate  of  copper,  and  place  each  in 
front  of  a  lantern,  so  as  to  project  two  colored  discs  on  the 
screen.  One  of  these  will  be  yellow  and  the  other  blue. 
Turn  the  lanterns  till  the  two  colored  discs  overlap  or  coin- 
cide. The  resulting  disc  is  white  (Figure  284).  In  this  case 
the  hues  are  mixed  without  any  mixture  of  substance. 

Now  mix  the  two  solutions  by  pouring  some  of  each 
into  a  third  cell,  and  place  this  cell  before  one  of  the  Ian- 


NATURAL   PHILOSOPHY.  265 

terns.  The  disc  on  the  screen  will  be  green.  The  same 
result  would  be  obtained  were  two  cells,  each  containing 
one  of  the  solutions,  placed  in  front  of  one  of  the  lanterns 
so  that  the  light  from  the  lantern  must  pass  through  both 
solutions. 

On  analyzing,  by  means  of  a  prism,  the  light  which 
passes  through  each  solution,  it  will  be  found  that  the 
yellow  solution  absorbs  and  quenches  all  the  rays  of  the 
spectrum  above  the  green  ;  and  the  blue  solution,  all  those 
below  the  green.  Green  is  the  only  color  which  is  not 
absorbed  by  either  substance.  Hence,  when  light  is  al- 
lowed to  pass  through  both  substances,  either  by  mixing 
them  in  one  cell,  or  by  placing  them  in  separate  cells,  one 
in  front  of  the  other,  they  absorb  and  quench  all  the  colors 
except  the  green,  and  therefore  the  disc  obtained  on  the 
screen  is  green.  The  hues  of  two  colored  substances  are 
never  blended  when  the  substances  themselves  are  mixed. 
One  of  the  substances  always  absorbs  and  quenches  a 
part  of  the  rays  which  escape  from  the  other. 

329.  The  Theory  of  Color  Perception.  — The  theory  of  color 
perception  at  present  accepted  by  nearly  all  authorities  is  that  of 
Young  modified  by  Helmholtz,  and  sometimes  called  the  Young- 
Helinholtz  theory.  According  to  this  theory  there  are  three 
primary  color-sensations,  namely,  those  of  red,  green,  and  violet, 
and  all  our  perceptions  of  color  arise  from  various  combinations 
of  these  three.  Each  minute  portion  of  the  retina  is  capable  of 
receiving  and  transmitting  these  three  sensations,  because  it  is 
supplied  with  three  nerve  fibrils,  one  of  which  is  especially 
adapted  for  the  reception  of  each  of  these  sensations.  "  One 
set  of  these  nerves  is  strongly  acted  on  by  long  waves  of  light, 
and  produces  the  sensation  we  call  red ;  another  set  responds 
most  powerfully  to  waves  of  medium  length,  producing  the  sen- 
sation which  we  call  green  ;  and,  finally,  the  third  set  is  strongly 
stimulated  by  short  waves,  and  generates  the  sensation  known 
as  violet.  The  red  of  the  spectrum,  then,  acts  powerfully  on 
the  first  set  of  these  nerves  ;  but,  according  to  the  theory,  it  also 


266 


NATURAL   PHILOSOPHY. 


acts  upon  the  other  two  sets,  but  with  less  energy.  The  same 
is  true  of  the  green  and  violet  rays  of  the  spectrum ;  they  each 
act  on  all  three  sets  of  nerves,  but  most  powerfully  on  those 
especially  designed  for  their  reception.  All  this  will  be  better 
understood  by  the  aid  of  the  accompanying  diagram  (Figure  285). 

Fig.  285. 


Along  the  horizontal  lines  i,  2,  3,  are  placed  the  colors  of  the 
spectrum  properly  arranged,  and  the  curves  above  them  indicate 
the  degree  to  which  the  three  kinds  of  nerves  are  acted  on  by 
these  colors.  Thus  we  see  that  nerves  of  the  first  kind  are 
powerfully  stimulated  by  red  light,  are  much  less  affected  by 
yellow,  still  less  by  green,  and  very  little  by  violet  light.  Nerves 
of  the  second  kind  are  much  affected  by  green  light,  less  by 
yellow  and  blue,  and  still  less  by  red  and  violet.  The  third  kind 
of  nerves  answer  readily  to  violet  light,  and  are  successively 
less  affected  by  other  kinds  of  light  in  the  following  order : 
blue,  green,  yellow,  orange,  red.  The  'next  point  in  the  theory 
is  that,  if  all  three  sets  of  nerves  are  simultaneously  stimulated 
to  about  the  same  degree,  the  sensation  which  we  call  white  will 
be  produced."  *  Therefore,  when  the  first  and  second  sets  of 
nerves  are  both  excited  more  or  less  powerfully  at  the  same 
time,  the  resulting  sensation  will  be  compound,  being  made 
up  of  the  sensation  of  red  and  green.  The  hue  perceived  in 
this  case  will  be  somewhere  between  the  red  and  the  green.  If 
the  two  compound  sensations  are  equally  intense,  the  hue  will 
lie  midway  between  red  and  green,  and  will  be  yellow.  If  the 
red  sensation  is  the  more  powerful,  the  hue  perceived  will  be 
nearer  the  red;  if  the  green  sensation  is  the  more  powerful, 
nearer  the  green.  In  a  similar  way,  when  the  second  and  third 
*  Rood's  Modern  Chromatics. 


NATURAL   PHILOSOPHY.  267 

sets  of  nerves  are  stimulated  together,  the  resulting  sensation 
will  be  compounded  of  a  sensation  of  green  and  of  violet.  The 
hue  perceived  will  lie  between  green  and  violet,  and  nearer  the 
one  or  the  other  of  these  colors  according  as  the  one  or 
the  other  of  the  component  sensations  is  the  more  intense.  So 
also  the  sensation  of  purple  results  from  the  blending  of  the 
two  sensations  of  red  and  violet.  Whether  the  hue  is  reddish 
purple  or  bluish  purple  depends  upon  whether  the  first  or  the 
third  set  of  nerves  is  more  powerfully  excited. 

According  to  the  Young-Helmholtz  theory,  all  color  sensa- 
tions, except  those  of  red,  green,  and  violet,  are  compound. 
These  compound  sensations  may,  however,  be  excited  by  a 
simple  external  agent.  For  instance,  a  single  set  of  luminous 
waves,  of  a  length  midway  between  those  of  red  and  green, 
would,  on  entering  the  eye,  excite  the  first  and  second  set  of 
nerves  equally,  and  so  give  rise  to  the  compound  sensation  of 
yellow.  The  eye  would  be  unable  to  distinguish  the  sensation 
thus  produced  from  one  produced  by  red  and  green  rays  enter- 
ing the  eye  together.  In  a  similar  way  the  sensation  of  any 
hue  between  the  red  and  the  green,  or  between  the  green  and 
the  violet,  may  be  awakened  either  by  a  single  set  of  waves  or 
by  two  sets  of  waves. 

The  sensation  of  white  is  composed  of  the  three  fundamental 
sensations  of  red,  green,  and  violet,  but  this  sensation  may  be 
awakened  by  two  hues,  or  even  by  two  sets  of  waves.  Were 
two  sets  of  waves  about  midway  between  the  red  and  the  green 
and  between  the  green  and  the  violet  to  enter  the  eye  at  the 
same  time,  they  would  excite  all  three  sets  of  nerve  fibres  and 
give  rise  to  the  sensation  of  white. 

330.  Color- Blindness.  —  There  are  many  persons  who 
cannot  see  certain  colors.  Such  persons  are  said  to  be 
color-blind.  Color-blindness  usually  takes  the  form  of  red 
blindness,  though  there  are  some  eyes  that  are  blind  to 
green,  and  others  that  are  blind  to  violet.  A  red-blind 
person  can  see  no  difference  in  color  between  a  ripe  straw- 
berry and  its  leaf.  His  range  of  hues  is  limited  to  green 
and  blue,  and  the  hues  produced  by  their  combinations. 


268  NATURAL   PHILOSOPHY. 

Such  a  person  will  make  the  most  absurd  mistakes  in  at- 
tempting to  match  colors,  mistaking  a  bright  scarlet  for  a 
black.  As  the  danger  signal  is  everywhere  a  red  light, 
serious  accidents  have  occasionally  been  traced  to  color- 
blindness in  those  employed  to  observe  the  signals. 

Many  persons  are  color-blind  without  being  aware  of  the 
fact.  This  defect  in  the  sight  can  often  be  detected  only 
by  systematic  testing  in  the  matching  of  colors. 

It  has  been  ascertained  that  about  one  male  in  every 
twenty-five  is  more  or  less  color-blind.  Comparatively  few 
women  are  color-blind. 

According  to  the  Young-Helmholtz  theory,  color-blindness  is 
due  to  the  absence  or  the  paralysis  of  one  or  other  of  the  three 
sets  of  nerve  fibres. 

II.  COLORS  PRODUCED  BY  ABSORPTION  AND  INTERFERENCE. 

331.  Colors  produced  by  Absorption,  —  Most  of  the  colors 
of  non-luminous  bodies  are  produced  by  absorption.  A 
small  portion  of  the  light  that  falls  upon  the  body  is  dif- 
fused at  the  surface.  The  portion  thus  diffused  enables 
us  to  see  the  surface,  and  is  white  or  the  color  of  the  inci- 
dent light.  A  large  portion  of  the  light  is  diffused  from 
particles  in  the  interior  after  it  has  penetrated  the  sub- 
stance of  the  body  to  a  slight  depth.  A  portion  of  this 
light  is  absorbed  and  quenched  in  its  passage  through  the 
substance  of  the  body.  It  is  this  light  which  gives  the 
body  its  color.  The  light  which  emerges  from  the  body 
after  the  internal  diffusion  will  be  the  light  which  enters 
the  body  minus  that  which  has  been  quenched  by  absorp- 
tion. The  color  of  the  body  will  be  the  color  which  is 
produced  by  the  blending  of  the  hues  which  remain  in  the 
light  after  it  has  suffered  absorption  by  the  body.  It  will  be 
the  complement  of  the  color  absorbed  by  the  body.  Bod- 
ies differ  in  color  because  they  absorb  different  constituents 
of  the  white  light  that  falls  upon  them,  or  else  the  same 


NATURAL   PHILOSOPHY.  269 

constituents  in  different  proportions.  In  either  case  the 
hue  of  the  light  which  escapes  from  the  body  will  be  dif- 
ferent. A  painter  does  not  create  colors.  He  simply  pre- 
pares the  surface  of  his  canvas  so  that  it  shall  destroy  all 
the  colors  of  white  light  which  he  does  not  want.  He 
produces  the  hue  he  desires  by  destroying  its  complement. 
Many  bodies  do  not  have  the  same  color  by  gaslight  as  by 
daylight.  Some  of  the  constituents  of  daylight  are  par- 
tially or  wholly  wanting  in  gaslight.  Hence  the  constit- 
uents which  remain  after  absorption  are  not  the  same  in  the 
two  cases.  Luminous  sodium  vapor  emits  only  yellow  rays; 
Most  colors  disappear  entirely  in  the  light  of  the  sodium 
flame  alone ;  for  in  case  the  body  absorbs  the  yellow  rays, 
there  are  no  rays  remaining  for  it  to  diffuse.  Strictly 
speaking,  the  color  does  not  reside  in  the  body,  but  in  the 
light  which  it  diffuses.  A  body  has  no  color  in  the  dark. 

332.  The  Colors  of  Soap-Bubbles.  —  Brilliant  colors  play  over 
the  surface  of  a  soap-bubble  while  it  lasts,  becoming  richer  and 
richer  as  the  bubble  becomes  thinner.  If  a  film  of  soap-suds  is 
held  on  a  ring  before  the  lantern,  so  as  to  throw  a  beam  of  re- 
flected light  upon  a  projecting  lens,  an  image  of  the  film  will  be 
projected  upon  the  screen  and  will  appear  highly  colored.  The 
colors  will  be  in  constant  motion.  These  brilliant  colors  are 
produced  by  interference.  Some  of  the  rays  of  light  which  fall 
upon  the  film  will  be  reflected  from  each  surface.  The  rays 
which  are  reflected  from  the  rear  surface  of  the  film  will  have 
to  travel  twice  the  thickness  of  the  film  farther  than  those  which 
are  reflected  from  the  front  surface.  Were  the  thickness  of  the 
film  one  fourth  of  a  wave-length,  the  rays  reflected  from  the  rear 
surface  of  the  film  would  fall  half  a  wave-length  behind  those 
reflected  from  the  front,  and  the  two  sets  would  be  in  opposite 
phases  on  leaving  the  front  of  the  film  after  reflection.  They 
would  consequently  destroy  each  other.  The  same  would  be 
true  were  the  thickness  of  the  film  any  odd  number  of  quarter 
wave-lengths. 

On  the  contrary,  were  the  thickness  of  the  film  half  of  a  wave- 
length, one  set  of  rays  would  fall  a  whole  wave-length  behind 


270  NATURAL    PHILOSOPHY. 

the  other  set,  so  that  the  two  sets  of  rays  would  be  in  the  same 
phase  on  their  return,  and  would,  accordingly,  intensify  each 
other.  They  would  also  be  in  the  same  phase  were  the  thick- 
ness of  the  film  any  even  number  of  quarter  wave-lengths. 

Now  the  thickness  of  the  film  is  constantly  changing  at  any 
one  point,  and  is  different  at  different  points.  Hence  the  two 
sets  of  rays  will  tend  to  destroy  each  other  at  some  points  and 
to  intensify  each  other  at  other  points  ;  and  at  any  one  point 
they  will  tend  to  intensify  each  other  one  instant,  and  to  destroy 
each  other  the  next.  Moreover,  as  the  waves  of  the  different 
colors  differ  in  length,  at  the  point  where  one  kind  of  waves  tend 
to  destroy  each  other,  other  kinds  of  waves  would  tend  to  in- 
tensify each  other.  The  destruction  of  a  portion  of  the  con- 
stituents of  white  light  by  interference  in  certain  parts  of  the 
film  gives  rise  to  the  phenomenon  of  color.  As  the  film  Changes 
in  thickness,  the  colors  shift  from  point  to  point  and  so  appear 
ir)  constant  motion. 

Any  thin  film  whatever  will  produce  these  colors. 
333-  Diffraction  Fringes.  —  When  a  bright  line  of  light  is 
looked  at  through  a  narrow  opening,  a  bright  band  of  white  light 
will  be  seen  at  the  centre  of  the  opening,  and,  parallel  with  this 
on  each  side,  a  number-  of  colored  fringes.  These  colored 
fringes  are  called  diffraction  fringes.  The  narrower  the  open- 
ing the  broader  the  fringes.  The  fringes  are  due  to  interference. 
As  each  wave  of  the  ether  passes  through  the  opening,  it  not 
only  pursues  its  direct  course  to  the  retina,  but  also  diverges  to 
the  right  and  the  left,  tending  to  put  in  motion  the  whole  mass 
of  ether  behind  the  opening.  Every  point  of  the  wave  which 
fills  the  opening  is  itself  the  centre  of  a  new  wave-system, 
which  is  transmitted  in  every  direction  through  the  ether  behind 
the  opening.  These  new  waves  would  meet  in  opposite  phases 
and  destroy  each  other  at  certain  points. 

Fi    2g6  Suppose,  at  first,  all  the  waves 

which  pass  through  the  opening 
are  of  the  same  length,  or,  in 
other  words,  that  the  light  is 
monochromatic.  Let  A  B  (Fig- 
ure 286)  be  an  enlarged  section 
of  the  opening,  and  m  n  a  por- 


NATURAL    PHILOSOPHY.  271 

tion  of  the  retina.  Consider  first  the  point  R  directly  in  front 
of  the  opening.  As  the  opening  is  very  narrow,  the  paths  by 
which  all  of  the  rays  starting  between  A  and  B  reach  the  point 
R  will  be  virtually  of  the  same  length.  Hence  there  will  be  no 
destruction  of  waves  at  this  point,  which  will  therefore  appear 
bright.  The  interference  of  the  rays  will  be  but  slight,  for  some 
distance  to  the  right  and  left  of  R.  Hence  there  will  be  a 
bright  band  at  this  central  point. 

Next  consider  the  point  R  (Figure  287)  so  situated  that  the 
paths  A  R  and  B  R,  by  which  rays  from  A  and  B  reach  it,  differ 
by  one  wave-length.  Draw  C R  flg  2g7- 

from  the  point  C,  half-way  between 
A  and  B.  Also  draw  Bfso  as  to 
make  //?  equal  to  B  R,  and  Ce 
parallel  to  it.  Af  will  be  the 
length  of  a  wave,  and  A  e,  ef,  and 
cd  each  the  length  of  half  a  wave. 
A  R  will  be  half  a  wave-length  longer  than  C  R,  and  every  ray 
from  A  to  C  will  be  just  half  a  wave-length  longer  than  every 
corresponding  ray  from  C  to  B.  Hence  the  two  sets  of  rays 
will  meet  in  opposite  phases  at  R,  and  will  accordingly  destroy 
each  other.  The  point  R  will  therefore  be  dark.  The  destruc- 
tion of  the  rays  will  be  nearly  complete  for  some  distance  each 
side  of  R.  Hence  there  will  be  a  dark  space  at  this  point. 
There  will  also  be  a  dark  space  at  the  corresponding  point  on 
the  left  of  the  opening. 

Suppose  the  point  R  (Figure  288)  so  situated  that  the  paths 
A  R  and  B  R  by  which  rays  from  A  and  B  would  reach  R,  would 
differ  by  a  wave-length  and  a  half  Fig 

in  length.  Take  the  two  points 
C  and  D  so  as  to  divide  the 
opening  into  three  equal  parts. 
Draw  CR  and  D  R.  Also  draw 
Bg  so  as  to  makegfi  equal  to 
BR,  and  draw  Df  and  Ce  par-  *~ 
allel  to  Bg.  Af  is  the  length  of  a  wave,  and  A  e  of  half  a 
wave.  The  rays  between  A  and  C  would  meet  those  between 
C  and  D  at  R  in  opposite  phases,  and  destroy  them  ;  while  the 
rays  between  D  and  B  would  not  be  destroyed  at  R.  Hence 


272  NATURAL   PHILOSOPHY. 

this  point  would  be  bright,  and  the  brightness  would  continue 
a  little  way  on  each  side  of  K.  The  corresponding  point  on  the 
left  of  the  opening  would  also  be  bright. 

In  a  similar  way  it  may  be  shown  that  there  would  be  com- 
plete destruction  of  the  rays  at  every  point  whose  distance  from 
the  two  edges  of  the  opening  differ  by  any  even  number  of  half 
wave-lengths,  and  only  partial  destruction  of  the  rays  at  every 
point  whose  distance  from  the  two  edges  of  the  opening  differ 
by  any  odd  number  of  half  wave-lengths. 

The  longer  the  waves,  the  farther  to  the  right  or  the  left  the 
points  at  which  there  would  be  only  partial  destruction  of  the 
waves.  Hence,  when  white  light  is  allowed  to  pass  through 
the  opening,  the  different  rays  will  produce  bright  bands  at 
different  distances  to  the  right  or  the  left  of  the  central  line,  the 
blue  being  nearest  to  the  central  line  and  the  red  the  farthest 
away  from  it.  The  fact  that  these  various  colored  bands  only 
partially  coincide  accounts  for  the  colors  of  the  fringe. 

Fine  lines  ruled  on  glass  or  polished  metal  reflect  light  from 
their  sides.  At  certain  points  the  rays  reflected  from  the  oppo- 
site sides  of  the  lines  meet  in  opposite  phases  and  destroy  each 
other.  The  obliquity  of  reflection  which  extinguishes  the 
shorter  wave  will  not  extinguish  the  longer  ones.  Hence  colors 
are  produced  whenever  light  is  reflected  from  finely  ruled  sur- 
faces. These  are  called  the  colors  of  striated  surfaces.  They 
are  beautifully  illustrated  by  mother-of-pearl.  This  shell  is 
composed  of  exceedingly  thin  layers,  which,  when  cut  across  in 
the  polishing  of  the  shell,  expose  their  edges,  and  furnish  the 
necessary  small  and  regular  grooves. 

334.  Diffraction  Spectrutn.  —  If  a  piece  of  glass,  ruled  with 
fine  lines  at  the  rate  of  several  thousand  to  the  inch,  is  held 
between  the  eye  and  a  bright  line,  so  that  the  lines  on  the  glass 
shall  be  parallel  with  the  lines  of  light,  a  number  of  spectra  are 
seen  on  each  side  of  the  central  line.  A  piece  of  glass  ruled  in 
this  way  is  called  a  grating,  and  the  spectra  obtained  with  it  are 
called  diffraction  spectra.  These  spectra  may  be  viewed  with 
a  telescope  instead  of  the  naked  eye. 

The  diffraction  spectrum  is  less  brilliant  than  the  prismatic 
spectrum,  but  it  is  of  far  greater  purity,  and  the  position  of  the 
colors  in  it  depends  solely  on  their  wave-lengths.  This  spec- 


NATURAL    PHILOSOPHY.  273 

trum  furnishes  the  most  accurate  method  of  ascertaining  the 
wave-lengths  of  the  different  colors. 

///.    COLORS  PRODUCED  BY  POLARIZATION. 

335.  Polarization  by  Plates  of  Tourmaline.  —  Tourmaline  is 
a  semi-transparent  mineral,  which  occurs  in  crystals.  A  plate 
cut  from  one  of  these  crystals,  with  its  faces  parallel  to  the  axis 
of  the  crystals,  is  equally  transparent  to  ordinary  light  in  what- 
ever position  it  is  held.  When  two  such  plates  of  tourmaline 
are  placed  together,  as  shown  in  Figure  289,  the  combina- 
tion will  be  most  transparent  when  the  plates  are  parallel  to 
each  other,  less  transparent  when  they  are  oblique  to  each 
other,  and  wholly  opaque  when  they  are  at  right  angles  to  each 
other.  The  light  which  has  passed  through  one  of  the  plates 

Fig.  289. 


of  tourmaline  is  in  a  peculiar,  unsymmetrical  condition.  It 
has  acquired  a  kind  of  two-sidedness,  so  that  it  will  pass  through 
a  second  plate  of  tourmaline  in  two  positions  180°  apart,  in 
which  the  second  plate  is  parallel  with  the  first,  and  be  stopped 
in  two  positions  90°  from  the  former,  in  which  the  second  plate 
is  at  right  angles  to  the  first.  Light  in  this  condition  is  said  to 
be  polarized. 

Polarized  light  cannot  be  distinguished  from  ordinary  light  by 
the  unaided  eye.  In  all  experiments  in  polarization,  two  pieces 
of  apparatus  must  be  employed,  one  to  produce  polarization, 
and  one  to  show  it.  The  former  is  called  the  polarizer,  and  the 
latter  the  analyzer.  Any  apparatus  that  will  serve  for  one  will 
serve  for  the  other  also.  In  the  case  of  the  tourmaline  plates, 
the  plate  which  first  receives  the  light  is  the  polarizer,  and  the 
other  plate  the  analyzer.  The  usual  method  of  testing  light  to 
see  whether  it  is  polarized  or  not  is  to  allow  it  to  fall  upon  an 
analyzer,  and  notice  whether  any  change  of  brightness  occurs  as 


274  NATURAL    PHILOSOPHY. 

the  analyzer  is  rotated.  When  the  light  of  the  blue  sky  is  exam- 
ined with  an  analyzer,  a  difference  of  brightness  can  be  detected 
as  the  analyzer  is  rotated,  especially  when  we  look  90°  from  the 
sun.  In  all  cases  in  which  light  is  polarized,  there  are  two  posi- 
tions of  the  analyzer,  differing  by  180°,  which  give  a  minimum 
of  light,  and  two  positions  midway  between  these  which  give  a 
maximum  of  light.  The  difference  between  the  maximum  and 
minimum  brightness  shows  the  completeness  of  the  polarization 
of  the  light. 

336.  The    Theory  of  Polarization.  —  The   following   state- 
ment of  the  theory  of   polarization,  as  applied  to  the  tourma- 
line  plates,   is   taken   from   Tyndall :    "It    has    been    already 
explained  that  the  vibrations  of  the  individual   ether-particles 
are  executed  across  the  line  of  propagation.      In  the  case  of 
ordinary  light  we  are  to  figure  the  ether-particles  as  vibrating 
in  all  directions,  or  azimuths,  as  it  is  sometimes  expressed,  across 
this  line.     Now,  in  the  case  of  a  plate  of  tourmaline  cut  parallel 
to  the  axis  of  the  crystal,  a  beam  of  light  incident  upon  the  plate 
is  divided  into  two,  the  one  vibrating  parallel  to  the  axis  of  the 
crystal,  the  other  at  right  angles  to  the  axis.     The  grouping  of 
the  molecules  reduces  all  the  vibrations  incident  upon  the  crys- 
tal to  these  two  directions.     One  of  these  beams  —  namely,  that 
whose  vibrations  are  perpendicular  to  the  axis  —  is  quenched 
with   exceeding   rapidity  by  the  tourmaline.      To   such  vibra- 
tions many  specimens  of  the  crystal  are  highly  opaque ;  so  that, 
after  having  passed  through  a  very  small  thickness  of  the  tourma- 
line, the  light  emerges  with  all  its  vibrations  reduced  to  a  single 
plane.       In  this  condition   it  is  what  we  call  plane  polarized 
light." 

In  every  case  of  plane  polarization  the  molecules  of  the  ether 
are,  according  to  the  undulatory  theory  of  light,  all  made  to 
vibrate  in  the  same  plane. 

337.  Polarization    by    Reflection.  —  Transmission    through 
tourmaline  is  only  one  of  several  ways  in  which  light  can  be 
polarized      When  a  beam  of  light  is  reflected  from  a  polished 
surface  of  glass,  wood,  ivory,  leather,  or  any  other  non-metallic 
substance,  at  an  angle  of  incidence  from  50°  to  60°,  it  is  more 
or  less  polarized,  and  in  like  manner  a  reflector  composed  of  any 
of  these  substances  may  be  employed  as  an  analyzer.     In  so 


NATURAL    PHILOSOPHY. 


275 


using  it,  it  is  rotated  about  an  axis  parallel  to  the  rays  which  are 
to  be  tested ;  and  the  observation  consists  in  noticing  whether 
this  rotation  produces  changes  in  the  amount  of  reflected  light. 

Malus's  polariscope  (Figure  290)  consists  of  two  reflectors, 
A,B,  —  one  serving  as  the  polarizer  and  the  other  as  the  ana- 
lyzer, —  each  consisting  of  a  pile  of  glass  plates.  Each  of  these 
reflectors  can  be  turned  about  a  Fig.  290. 

horizontal  axis  ;  and  the  upper  one 
(which  is  the  analyzer)  can  also  be 
turned  about  a  vertical  axis,  the 
amount  of  rotation  being  meas- 
ured  on  the  horizontal  circle  C  C. 
To  obtain  the  most  powerful 
effects,  each  of  the  reflectors 
should  be  set  at  an  angle  of  about 
33°  to  the  vertical,  and  a  strong 
beam  of  common  light  should  be 
allowed  to  fall  upon  the  lower  pile 
in  such  a  direction  as  to  be  reflected  vertically  upwards.  It  will 
thus  fall  upon  the  centre  of  the  upper  pile,  and  the  angles  of 
incidence  and  reflection  on  both  piles  will  be  about  57°.  The 
observer,  looking  into  the  upper  pile  in  such  a  direction  as 
to  receive  the  reflected  beam,  will  find  that,  as  this  pile  is 
rotated  about  a  vertical  axis,  there  are  two  positions  (differing 
by  180°)  in  which  he  sees  a  black  spot  in  the  centre  of  the  field 
of  view,  these  being  the  positions  in  which  the  upper  pile  re- 
fuses to  reflect  the  light  reflected  to  it  from  the  lower  pile. 
They  are  90°  on  either  side  of  the  position  in  which  the  two 
piles  are  parallel ;  this  latter,  and  the  position  differing  from 
it  by  1 80°,  being  those  which  give  a  maximum  of  reflected 
light. 

For  every  reflecting  substance  there  is  a  particular  angle  of 
incidence,  which  gives  a  maximum  of  polarization  in  the  re- 
flected light.  It  is  called  the  polarizing  angle  for  the  substance, 
and  is  that  particular  angle  of  incidence  which  is  the  comple- 
ment of  the  angle  of  refraction,  so  that  the  refracted  and 
reflected  rays  are  at  right  angles.  This  important  law  was 
discovered  experimentally  by  Sir  David  Brewster. 

The  reflected  ray,  under  these  circumstances,  is  in  a  state  of 


276  NATURAL   PHILOSOPHY. 

almost  complete  polarization  ;  and  the  advantage  of  employing 
a  pile  of  plates  consists  merely  in  the  greater  intensity  of  the 
reflected  light  thus  furnished.  The  transmitted  light  is  also 
polarized  :  it  diminishes  in  intensity,  but  becomes  more  com- 
pletely polarized,  as  the  number  of  plates  is  increased.  The 
reflected  and  the  transmitted  light  are  in  fact  mutually  comple- 
mentary, being  the  two  parts  into  which  common  light  has  been 
decomposed ;  and  their  polarizations  are  accordingly  opposite, 
so  that,  if  both  the  transmitted  and  reflected  beams  are  exam- 
ined by  a  tourmaline,  the  maxima  of  obscuration  will  be  obtained 
by  placing  the  axis  of  the  tourmaline  in  the  one  case  parallel  and 
in  the  other  perpendicular  to  the  plane  of  incidence. 

338.  Polarization  by  Double  Refraction.  —  When  a  ray  of 
light  passes  through  a  crystal  of  Iceland  spar,  it  is  usually  di- 
vided into  two  rays,  or  doubly  refracted.  One  of  these  rays  obeys 
the  law  of  ordinary  refraction,  and  is  called  the  ordinary  ray  ; 
the  other  ray  obeys  a  different  law,  and  is  called  the  extraor- 
dinary ray.  As  a  rule,  transparent  crystals  doubly  refract  light. 
Both  of  the  rays  furnished  by  double  refraction  are  polarized,  the 
polarization  in  this  case  being  more  complete  than  in  any  of  the 
cases  thus  far  discussed.  On  looking  at  the  two  images  through 
a  plate  of  tourmaline,  or  any  other  analyzer,  it  will  be  found  that 
they  undergo  great  variations  of  brightness  as  the  analyzer  is  ro- 
tated, one  of  them  becoming  fainter  whenever  the  other  becomes 
brighter,  and  the  maximum  brightness  of  either  being  simulta- 
neous with  the  absolute  extinction  of  the  other.  If  a  second 
piece  of  Iceland  spar  is  used  as  the  analyzer,  four  images  will 
be  seen,  of  which  one  pair  becomes  dimmer  as  the  other  pair 
becomes  brighter,  and  either  of  these  pairs  can  be  extinguished 
by  giving  the  analyzer  a  proper  position. 

Since  the  opposite  faces  of  a  rhomb  of  Iceland  spar  are  paral- 
lel, the  ordinary  and  extraordinary  rays  emerge  from  the  crystal 
parallel  to  the  incident  ray  and  to  each  other,  but  quite  near  to- 
gether. If,  however,  the  crystal  is  cut  into  the  form  of  a  prism 
in  such  a  way  that  its  refracting  edge  may  be  parallel  to  its  axis, 
the  ordinary  and  extraordinary  rays,  after  leaving  the  prism,  will 
diverge,  so  that  we  may  easily  insulate  either  and  examine  it 
separately.  Such  a  prism  will,  of  course,  disperse  both  rays  so 
as  to  produce  spectra  ;  but  it  may  be  rendered  sufficiently  achro- 


NATURAL    PHILOSOPHY. 


277 


matic  by  combining  with  it  a  second  prism  of  glass, 
whose  dispersive  power  is  different  from  that  of  the 
crystal.  This  prism  is  called  a  double-refracting 
prism,  and  is  usually  mounted  as  shown  in  Figure 
291.  This  prism  may  be  used  either  as  a  polarizer 
or  as  an  analyzer. 

If  a  rhomb  of  Iceland  spar  is  cut  through  along  the  diagonal 
plane  abed  (Figure  292),  and  the  cut  faces  are  cemented  to- 
gether with  Canada  balsam,  it  forms  what  is  known  as  a  Nicol's 
prism,  from  the  name  of  the  inventor.  The 
ray  SI  5s  doubly  refracted  on  entering  the 
prism.  The  ordinary  ray  is  totally  re- 
flected on  meeting  the  surface  of*  the  bal- 
sam, and  passes  out  through  the  side  of  the 
prism  at  o.  The  extraordinary  ray  passes 
through  the  balsam,  and  finally  emerges 
from  the  end  of  the  prism  in  the  direction 
of  ce,  parallel  to  the  original  direction  SI. 
This  prism  is  the  most  effective  polarizer  or 
analyzer  yet  constructed. 

338 .  Colors  produced  by  Polarization.  — 
Very  beautiful  colors  may  be  produced  by 

the  peculiar  action  of  polarized  light.  If  a  thin  film  of  selenite 
is  placed  between  two  Nicol  prisms  through  which  a  power- 
ful beam  of  light  is  passing,  the  image  of  the  film  glows  with  the 
richest  colors.  If  we  turn  the  front  Nicol,  the  colors  gradually 
fade  and  disappear,  and  again  reappear  in  complementary  hues. 
When  the  film  is  of  uniform  thickness,  the  color  is  uniform  ;  but 
if  the  thickness  of  the  film  varies,  some  parts  of  the  film  appear 
of  one  color  and  some  of  another.  The  shape  and  thickness  of 
the  film  may  be  varied  so  as  to  exhibit  flowers  and  other  objects 
in  hues  unattainable  by  art.  These  colors  are  all  produced  by 
interference. 

IV.   PHOSPHORESCENCE. 

339.  Phosphorescence   and  Fluorescence.  —  Certain    sub- 
stances, after  exposure   to  sunlight,  will  appear  luminous 
for  a  long  time  in  the  dark,  and  that  without  any  signs  of 
combustion  or   of  elevation   of    temperature.     Such   sub- 


278  NATURAL    PHILOSOPHY. 

stances  are  said  to  be  phosphorescent.  The  sulphides  of 
calcium  and  of  barium  possess  this  property  to  a  remarka- 
ble degree,  and  are  therefore  employed  in  the  manufacture 
of  luminous  paint.  Very  many  substances  are  phospho- 
rescent to  a  slight  degree,  their  phosphorescence  continuing, 
in  the  majority  of  cases,  only  a  fraction  of  a  second  after 
withdrawal  from  the  sun's  rays.  Phosphorescence  is  ex- 
cited by  the  violet  and  ultra-violet  rays. 

Fluorescence  is  essentially  the  same  as  phosphorescence. 
The  former  name  is  applied  to  the  phenomenon  observed 
while  the  body  is  actually  ^exposed  to  the  source  of  light, 
and  the  latter  to  the  phenomenon  observed  after  the  light 
from  the  source  is  cut  off.  Phosphorescence  is,  so  to  speak, 
a  kind  of  persistent  fluorescence.  Uranium  glass  is  a  very 
convenient  material  for  the  exhibition  of  fluorescence.  A 
thick  piece  of  it,  held  in  the  violet  or  ultra-violet  portion 
of  the  solar  spectrum,  is  filled  to  the  depth  of  from  ^  to 
^  of  an  inch  with  a  faint  nebulous  light.  A  solution  of 
sulphate  of  quinine  is  also  frequently  employed  f&r  exhibit- 
ing the  same  effect,  the  luminosity  in  this  case  being  bluish. 
If  the  solar  spectrum  is  thrown  upon  a  screen  freshly 
washed  with  sulphate  of  quinine,  the  ultra-violet  portion 
will  become  visible  by  fluorescence ;  and  if  the  spectrum 
is  very  pure,  the  presence  of  dark  lines  in  this  portion 
will  be  detected. 

H.   CONVERSION  OF  RADIANT  ENERGY  INTO  SOUND. 

340.  Bell's  Discovery.  —  Mr.  Graham  Bell  has  discovered 
that  musical  sounds  are  developed  when  an  intermittent  beam 
of  light  is  allowed  to  fall  upon  a  solid,  liquid,  or  gas  under  suita- 
ble conditions.  The  loudness  of  the  sound  varies  with  the 
nature  of  the  substance  employed  and  with  its  physical  condi- 
tion. A  thin  disc  of  a  solid  will  emit  a  louder  sound  than  a 
thick  mass.  The  loudest  sounds  are  produced  by  solids  in  a 
loose,  porous,  spongy  condition,  and  by  those  which  have  the 
darkest  and  most  absorbent  colors. 


NATURAL    PHILOSOPHY.  279 

The  solids  which  have  been  found  to  be  the  most  sensitive  to 
the  action  of  the  intermittent  beam  are  cotton-wool,  worsted, 
and  other  fibrous  materials,  cork,  sponge,  platinum,  and  other 
metals  in  the  spongy  condition,  and  lampblack. 

341.  BelFs  Explanation  of  the  Action  of  the  Intermittent 
Beam  upon  such  Substances.  —  "  Let  us  consider,  for  example, 
the  case  of  lampblack,  a  substance  which  becomes  heated  by 
exposure  to  rays  of  every  refrangibility.     I  look  upon  a  mass  of 
this  substance  as  a  sort  of  sponge,  with  its  pores  filled  with  air 
instead  of  water.     When  a  beam  of  sunlight  falls  upon  this 
mass,  the  particles  of  lampblack  are  heated,  and  consequently 
expand,  causing  a  contraction  of  the  air-spaces  or  pores  among 
them.     Under  these  circumstances  a  pulse  of  air  should  be  ex- 
pelled just  as  we  squeeze  water  out  from  a  sponge.     The  force 
with  which  the  air  is  expelled  must  be  greatly  increased  by  the 
expansion  of  the  air  itself,  due  to  contact  with  the  heated  par- 
ticles of  lampblack. 

"  When  the  light  is  cut  off,  the  converse  process  takes  place. 
The  lampblack  particles  cool  and  contract,  thus  enlarging  the 
air-spaces  among  them,  and  the  enclosed  air  also  becomes 
cooled.  Under  these  circumstances  a  partial  vacuum  would  be 
formed  among  the  particles,  and  the  outside  air  would  then  be 
absorbed,  as  water  is  by  a  sponge  when  the  pressure  of  the 
hand  is  removed. 

"  I  imagine  that  in  some  such  manner  as  this  a  wave  of  con- 
densation is  started  in  the  atmosphere  each  time  a  beam  of  sun- 
light falls  upon  the  lampblack,  and  a  wave  of  rarefaction  is 
originated  when  the  light  is  cut  off. 

"  We  can  thus  understand  how  it  is  that  a  substance  like 
lampblack  produces  intense  sonorous  "vibrations  in  the  sur- 
rounding air,  while  at  the  same  time  it  communicates  a  vary 
feeble  vibration  to  the  diaphragm  or  solid  bed  on  which  it  rests" 

Of  course  the  pitch  of  the  sound  emitted  in  any  case  depends 
upon  the  rapidity  with  which  the  beam  of  light  is  intercepted. 

342.  The  Radiophone.  — The  radiophone,  or  instrument  for 
producing  sound  by  radiant  energy,  consists  of  an  instrument 
for  transmitting  the  intermittent  beam,  called  the  transmitter, 
and  of  an  instrument  for  receiving  the  intermittent  beam,  called 
the  receiver. 


280 


NATURAL    PHILOSOPHY. 


One  form  of  the  transmitter  is  shown  in  Figure  293.     It  con- 
sists of  a  reflector  C,  and  of  a  rotating  disc  B.     The  disc  is 

Fig.  294. 


pierced  with  a  number  of  radial 
slits.  Sometimes  two  of  these 
discs  are  used,  one  fixed  and  the 
other  capable  of  rotation.  The 
beam  is  reflected  from  the  mirror 
upon  the  disc.  When  the  beam 
is  thrown  upon  only  one  point  of 
the  disc,  only  a  single  disc  is 
needed.  On  rotating  the  disc 
the  beam  is  transmitted  where  it 
falls  upon  a  slit  and  intercepted 
by  the  spaces  between  the  slits. 
The  more  rapidly  the  disc  is 
turned,  the  more  rapidly  the  beam 
is  intercepted.  When  the  beam 
is  reflected  upon  the  whole  disc, 
the  double  disc  is  necessary.  In 
this  case  the  beam  is  transmitted 
when  the  slits  of  the  rotating  disc 
are  opposite  those  of  the  fixed 
disc,  and  intercepted  when  the 


NATURAL   PHILOSOPHY.  281 

slits  of  the  rotating  disc  are  opposite  the  spaces  between  the 
slits  of  the  fixed  disc. 

One  form  of  the  receiver  is  shown  in  Figure  294.  It  consists 
of  a  parabolic  reflector  in  the  focus  of  which  is  placed  a  glass 
bulb  A  containing  the  lamp-black  or  other  sensitive  substance. 
The  light  is  reflected  from  the  mirror  C,  is  intercepted  by  the 
rotating  disc  B,  and  is  brought  to  a  focus  upon  the  bulb  at  A. 
The  bulb  A  is  connected  with  the  ear  by  means  of  a  hearing- 
tube. 

On  rotating  the  disc  £,  a  continuous  musical  note  is  heard, 
whose  pitch  rises  with  the  speed  of  the  rotation  of  the  disc. 
By  tilting  the  mirror  C  this  continuous  musical  note  may  be 
broken  up  into  long  and  short  intervals,  so  as  to  transmit  a 
message. 


Another  form  of  the  receiver  is  shown  in  Figure  295.  It 
consists  of  a  hollow  cone  of  brass,  closed  at  the  base  with  a 
flat  plate  of  glass,  and  connected  at  the  apex  with  an  ear-tube. 
The  sensitive  material  employed  is  enclosed  in  the  conical 
cavity.  Smoked  wire-gauze  in  the  receiver  gives  the  loudest 
sounds. 

343.  Sounds  produced  by  Different  Kinds  of  Rays.  —  In 
Figure  296  is  shown  a  kind  of  spectrophone,  or  instrument  for 
examining  the  power  of  the  rays  in  different  parts  of  the  spec- 
trum to  produce  sound.  The  rays  reflected  from  the  mirror  A 
are  brought  to  a  focus  by  the  lens  B  upon  the  opening  in  the 
screen  C,  and  there  dispersed  by  a  bisulphide  of  carbon  prism  E, 
suitably  placed  between  two  lenses.  The  rays  are  intercepted 
by  the  rotating  disc  F.  The  rays  are  then  examined  by  the 


282 


NATURAL    PHILOSOPHY. 


receiver  G,  having  a  small  opening  in  a  diaphragm  in  front  of 
the  glass  plate. 

On  using  the  smoked  wire-gauze  in  the  receiver,  it  is  found 


Fig.  296- 


that  sound  is  produced  by  all  the  rays 
of  the  spectrum  except  the  extreme  vio- 
let. The  sound  rises  in  intensity  as  the 
receiver  is  passed  from  the  violet  to  the 
red  end  of  the  spectrum,  and  attains  its 
maximum  far  out  in  the  ultra-red  region 
of  the  spectrum.  With  different  sub- 
stances in  the  receiver,  the  portion  of 
the  spectrum  capable  of  producing  au- 
dible sounds  is  found  to  vary  greatly, 
as  well  as  the  region  of  maximum  in- 
tensity of  sound.  From  numerous  ex-  - 
periments  Graham  Bell  has  arrived  at  the 
conclusion  that  "  the  nature  of  the  rays 
that  produce  sonorous  effects  in  different 
substances  depends  upon  the  nature  of 
the  substances  that  are  exposed  to  the 
beam,  and  that  the  sounds  are  in  every 
case  due  to  the  rays  of  the  spectrum  that 
are  absorbed  by  the  body" 

It  has  been  proposed  to  give  the 
name  radiophone  to  an  instrument  sen- 
sitive to  all  the  rays ;  and  the  names 
thermoplione,  photophone,  and  actino- 
phoneio  instruments  especially  sensitive 
to  thermal,  luminous,  and  actinic  rays 
respectively. 

344.  Sounds  produced  by  Vapors.  — 
Many  vapors  have  been  found  to  be 
especially  sensitive  to  the  action  of  the 
intermittent  beam.  Tyndall  was  one  of 
the  first  to  experiment  with  vapors.  He 
was  engaged  in  a  series  of  experiments 
*^  upon  the  absorbent  powers  of  different 

gases  when,  as   he  says,   "  I  became  acquainted  with  the  in- 
genious and  original  experiments  of  Mr.  Graham  Bell,  wherein 


NATURAL   PHILOSOPHY.  283 

musical  sounds  are  obtained  by  the  action  of  an  intermittent 
beam  of  light  on  solid  bodies.  From  the  first  I  entertained 
the  opinion  that  these  singular  sounds  were  caused  by  rapid 
changes  of  temperature,  producing  corresponding  changes  of 
shape  and  volume  in  the  bodies  impinged  upon  by  the  beam. 
But  if  this  be  the  case,  and  if  gases  and  vapors  really  ab- 
sorb radiant  heat,  they  ought  to  produce  sounds  more  intense 
than  those  obtainable  from  solids.  I  pictured  every  stroke 
of  the  beam  responded  to  by  a  sudden  expansion  of  the  ab- 
sorbent gas,  and  concluded  that,  when  the  pulses  thus  excited 
followed  each  other  with  sufficient  rapidity,  a  musical  note  must 
be  the  result.  .  .  .  Highly  diathermanous  bodies,  I  reasoned, 
would  produce  faint  sounds,  while  highly  athermanous  bodies 
would  produce  loud  sounds  :  the  strength  of  the  sound  being, 
in  a  sense,  the  measure  of  the  absorption."  He  found  the  re- 
sults of  his  experiments  to  be  in  exact  accordance  with  his 
theory. 

345.  The  Articulating  Photophone.  —  In  the  articulating 
photophoite  the  intensity  of  the  light  which  falls  upon  the  receiver 
is  made  to  vary  in  the  same  manner  as  the  vibration  of  the 
spoken  words.  To  accomplish  this  a  thin  piece  of  mica  is  used 
as  a  reflector,  and  is  placed  at  the  bottom  of  a  little  chamber, 
connected  with  the  mouth-piece  by  a  tube.  On  speaking  into 
the  mouth-piece  the  disc  of  mica  is  thrown  into  vibration. 
These  vibrations  change  the  form  of  the  reflecting  surface, 
making  it  more  or  less  convex  or  concave  as  the  case  may  be. 
Every  change  in  the  form  of  the  reflecting  surface  changes  the 
character  of  the  reflected  beam,  making  it  more  or  less  divergent 
or  convergent  as  the  case  may  be.  Every  change  of  this  kind 
in  the  character  of  the  reflected  beam  alters  the  intensity  of  the 
light  that  falls  upon  the  receiver. 

The  general  arrangement  of  these  instruments  is  shown  in 
Figure  297.  Words  spoken  at  A  are  repeated  at  B,  the  sound 
being  transmitted  not  by  pulsations  of  the  air,  but  by  pulsations 
of  the  reflected  beam. 


284 


NATURAL   PHILOSOPHY. 


V. 
MAGNETISM. 

346.  Magnets.  —  An.  iron  ore  was  in  ancient  times  found 
at  Magnesia,  in  Asia  Minor,  which  had  a  peculiar  property 
of  attracting  pieces  of  iron.     From  this  circumstance  this 
peculiar  property  of  attracting  iron  has  been  named  mag- 
netism, and  the  body  possessing  it  is  called  a  magnet.     A 
natural  magnet  is  now  usually  called  a  lodestone.     It  is  one 
of  the  oxides  of  iron,   and   is  very  abundant  in   nature. 
Artificial  magnets  are  bars  of  steel,  sometimes  straight  and 
sometimes  bent  in  the  shape  of  a  horse-shoe. 

347.  The   Poles   of   a   Magnet.  —  If    a   bar-magnet   be 
plunged  into  iron  filings  and   withdrawn,  the   filings   will 
cling  in   large   quantities  to  Fig.  298. 

the  ends  of  the  bar  and  leave 

the  middle  bare  (Figure  298). 

If  the  magnet  is  very  thick 

in  proportion  to   its  length, 

the  filings  will  adhere  to  all 

parts  of    it,  but  diminish  in 

quantity  rapidly  towards  the  middle.     The  force  of  the 

magnet  is  thus  seen  to  reside  chiefly  at  the  ends.     The 

ends  of  the  magnet  are  called  the  poles ;  and  the  middle 

line  of  the  bar,  where  magnetic  force  is  entirely  wanting, 

is  called  the  neutral  line. 

When  a  bar-magnet  is  suspended  so  as  to  turn  freely,  it 
will  take  a  north  and  south  direction,  one  end  of  the  bar 
always  turning  towards  the  north  and  the  other  towards 


286  NATURAL    PHILOSOPHY. 

the  south.  The  end  which  turns  towards  the  north  is 
called  the  north  or  marked  pole  of  the  magnet ;  and  the 
other  end,  the  south  or  unmarked  pole. 

If  the  marked  pole  of  a  magnet  is  presented  to  the 
marked  pole  of  another  magnet  which  is  free  to  turn, 
there  is  seen  to  be  repulsion  between  the  poles.  The  same 
is  true  if  the  unmarked  pole  of  one  magnet  is  presented 
to  the  unmarked  pole  of  another.  If  we  present  the 
marked  pole  of  one  magnet  to  the  unmarked  pole  of 
another,  we  see  attraction  between  the  poles.  Like  poles 
of  magnets  repel  each  other,  and  unlike  poles  attract  each 
other. 

Fig.  299- 

If  a  magnet  A  B  (Figure  299)  is  broken  into  any  num- 
ber of  pieces,  each  piece  will  be  a  complete  magnet  with 
two  poles,  each  of  the  strength  of  the  original  poles.  In 
each  of  the  four  pieces  into  which  the  magnet  in  the  figure 
is  represented  to  be  broken,  the  pole  to  the  left,  a,  is  the 
same  as  the  pole  A  at  the  left  end  of  the  original  magnet. 
Also  the  pole  b  at  the  right-hand  end  will  be  the  same  as 
the  pole  B  of  the  original  bar. 

Fig.  300. 


348.   Lines  of  Magnetic  Force.  —  Place  a  sheet  of  drawing- 
paper  stretched  on  a  frame  over  a  bar-magnet,  and    sift 


NATURAL    PHILOSOPHY.  287 

fine  iron  filings  upon  it.  If  we  tap  the  paper  gently,  the 
filings  will  arrange  themselves  in  a  system  of  curved  lines, 
as  shown  in  Figure  300.  If  a  horse-shoe  magnet  is  held 
under  the  paper  in  a  vertical  position  with  its  poles  against 
the  paper,  the  filings  will  form  the  system  of  curves  shown 
in  Figure  301.  These  curves  mark  the  lines  along  which 

Fig.  301. 


the  magnetic  force  acts,  and  show  the  direction  and  inten- 
sity of  the  force  at  each  point.  The  curves  are  nearest 
together  about  the  poles  of  the  magnet,  where  the  mag- 
netism is  most  intense.  The  space  in  the  neighborhood 
of  a  magnet  which  is  pervaded  by  its  force  is  called  the 
magnetic  field. 

349.  The  Curve  of  Magnetic  Intensity  in  a  Bar-Magnet.  — 
The  curved  line  A  MB  (Figure  302)  shows  the  relative 
intensity  of  the  magnetic  F ig.  302 

force  in  different  parts  of 
a  bar-magnet,  the  distance 
of  the  curve  from  each  point 
of  the  line  O  MX  represent-  " 
ing  the  intensity  of  the  force 
at  that  point.  Half  of  the 

curve  is  drawn  above  the  line  and  half  of  it  below  the 
line,  to  indicate  the  opposite  properties  of  the  two  halves 
of  the  bar. 


288  NATURAL    PHILOSOPHY. 

350.  Magnetic  Induction.  —  If  a  bar-magnet  is  brought 
near  a  piece  of  soft  iron,  it  develops  magnetism  in  it  by  an 
action  called  induction.  If  iron  filings  are  scattered  over 
the  soft  iron  while  under  the  influence  of  the  magnet,  they 
will  adhere  to  its  ends,  as  shown  in  Figure  303.  The  soft 

Fig.  303. 


iron  will  have  two  poles  and  a  neutral  portion  between 
them.  The  near  end  of  the  soft  iron  will  be  the  opposite 
pole  to  that  of  the  bar  presented  to  it ;  and  the  far  end, 
the  other  pole.  Remove  the  magnet,  and  the  iron  filings 
fall  off  from  the  piece  of  iron,  showing  that  the  iron  retains 
no  traces  of  magnetism,  or,  at  least,  only  very  slight  ones. 
The  attraction  of  pieces  of  iron  by  a  magnet  is  always 
preceded  by  induction,  the  magnet  developing  in  the  por- 
tion of  the  iron  nearest  it  a  magnetic  pole  unlike  its  own. 
Fig.  304.  Hence  pieces  of  iron  are  at- 

tracted with  equal  readiness 
by  either  pole  of  a  magnet. 
A  piece  of  iron  which  has 
become  magnetic  by  contact 
with  a  permanent  magnet 
may  attract  a  second  piece  of 
iron,  and  this  a  third,  and  so 
on  (Figure  304).  A  magnetic 
chain  may  thus  be  formed, 
each  component  of  which  has 
two  magnetic  poles.  Each 
piece  of  iron  in  the  filings 
which  cling  to  the  poles  of  a  magnet  becomes  a  magnet 


NATURAL    PHILOSOPHY.  289 

through  induction,  and  these  pieces  are  held  together  by 
their  dissimilar  poles. 

A  piece  of  steel  also  becomes  magnetic  by  induction 
when  acted  upon  by  a  magnet,  but  it  is  not  so  powerfully 
magnetized  as  the  soft  iron  It  is  harder  to  magnetize  the 
steel  than  the  iron,  but  the  steel  retains  its  magnetic  power 
after  the  magnet  has  been  withdrawn.  This  property  of 
retaining  magnetism  is  possessed  in  a  very  high  degree  by 
very  hard  steel,  and  scarcely  at  all  by  very  pure  and  soft 
iron. 

351.  Magnetization  of  Steel  Bars.  —  Permanent  magnets 
are  bars  of  steel.  The  steel  bar  may  be  magnetized  either 
by  the  method'  called  magnetization  by  single  touch,  or  by 
that  called  magnetization  by  double  touch. 

In  the  former  method,  the  bar  to  be  magnetized  is  laid 
on  a  board  (Figure  305),  near  one  end  of  which  is  a  stop 
whose  height  is  less  than  Fig.  305 

the  thickness  of  the  bar. 
The  magnet  is  held  in  a 
sloping  position  and  drawn 
over  the  bar  several  times, 
always  in  the  same  direc- 
tion and  with  the  same  end  downward.  If  the  marked 
end  of  the  magnet  is  held  downward  and  drawn  over  the 
bar  from  a  to  b,  the  end  a  will  become  a  marked  pole.  If 
the  magnet  is  drawn  over  the  bar  in  the  opposite  direction, 
or  the  other  pole  of  the  magnet  is  held  downward,  the 
end  b  will  become  the  marked  pole. 

In  the  method  by  double  touch,  two  magnets  are  held 
one  in  each  hand  with  dissimilar  poles  downward  over 
the  centre  of  the  bar  to  be  mag-  Fig-  3°6. 

netized,  as  shown  in  Figure.  306. 
They  are  now  drawn  apart  quite 
over  the  ends  of  the  bar,  lifted, 
and  replaced  at  the  centre  and 


290  NATURAL   PHILOSOPHY. 

again  drawn  over  the  ends.  This  process  is  repeated  sev- 
eral times.  The  end  of  the  bar  over  which  the  unmarked 
end  of  the  magnet  has  been  drawn  will  be  the  marked  pole, 
and  vice  versa. 

352.  Intensity  of  Magnetization.  —  The  same  steel  bar  may 
be  magnetized  more  or  less  intensely.  As  a  rule,  if  we  increase 
the  strength  of  the  magnetizing  magnet,  we  increase  the  mag- 
netization of  the  bar.  In  all  bars  there  is,  however,  a  certain 
limit,  after  which  no  amount  of  magnetic  force  can  increase 
their  permanent  magnetism.  This  is  called  their  saturation 
point,  and  bars  so  magnetized  are  said  to  be  magnetized  to 
saturation. 

It  is  possible  to  supersaturate  a  bar  with  magnetism,  that  is, 
to  give  it  temporarily  a  stronger  magnetization  than  it  can 
permanently  retain.  It  is  then  found  that,  after  the  inducing 
magnetic  force  is  removed,  the  magnetic  force  diminishes  at  a 
gradually  decreasing  rate  until  it  has  reached  its  permanent 
amount. 

The  lifting  power  of  a  magnet  generally  increases  with  its 
size,  but  small  magnets  are   usually  able  to  sustain  a  greater 
multiple  of  their  own  weight  than  large  ones.     Hence  it  has 
t    Q  been  found   advantageous  to  Fig.  308. 

construct  compound  magnets,     „    _     i^^g— =. 

consisting    of    a    number  of  ( 

thin   bars  laid   side  by  side, 

with    their   similar   poles   all 

pointing  the  same  way.    Fig- 
ure   307    represents    such    a 

compound  magnet  composed 

of  twelve    elementary    bars, 

arranged    in    three    rows   of 

four  bars  each.     Their  ends 

are  inserted  in  masses  of  soft 

iron,  the  extremities  of  which 

constitute   the   poles   of    the 

system. 

Figure  308  represents  a  compound  horse- 
shoe magnet,  whose  poles  N  and  6"  support 


NATURAL    PHILOSOPHY.  291 

a  keeper  of  soft  iron,  from  which  is  hung  a  bucket  for  holding 
weights.  By  adding  fresh  weights  day  after  day,  the  magnet 
may  be  made  to  carry  a  much  greater  load  than  it  could  have 
supported  originally  ;  but  if  the  keeper  is  torn  away  from  the 
magnet,  the  additional  power  is  instantly  lost,  and  the  magnet 
is  able  to  sustain  only  its  original  load. 

353.  Action  of  Magnetism  on  all  Bodies.  —  It  has  long  been 
known  that  iron  and  steel  are  not  the  only  substances  which  can 
be  acted  on  by  magnetism.  Nickel  and  cobalt,  especially,  were 
known  to  be  attracted  by  a  magnet,  though  very  much  more 
feebly  than  iron,  while  bismuth  and  antimony  were  repelled. 
Faraday  showed  that  all,  or  nearly  all,  substances,  whether 
solid,  liquid,  or  gaseous,  are  susceptible  of  magnetic  influence, 
and  that  they  can  all  be  arranged  in  one  or  the  other  of  two 
classes,  characterized  by  opposite  qualities.  This  opposition  of 
quality  is  manifested  in  two  ways. 

(i.)  As  regards  attraction  and  repulsion,  iron  and  other 
paramagnetic  bodies  are  attracted  by  either  pole  of  a  magnet, 
or  more  generally,  they  tend  to  move  from  places  of  weaker  to 
places  of  stronger  force.  On  the  other  hand,  bismuth  and  other 
diamagnetic  bodies  are  repelled  by  either  pole  of  a  magnet,  and 
in  general  tend  to  move  from  places  of  stronger  to  places  of 
weaker  force. 

(2.)  As  regards  orientation,  a  paramagnetic  body  when  sus- 
pended between  the  poles  of  a  magnet  places  itself  axially, 
that  is  to  saj,  tends  to  place  its  length  along  the  line  joining  the 
poles,  or  more  generally,  when  put  in  any  magnetic  field,  tends 
to  place  its  length  along  the  line  of  force  ;  hence  the  name 
^//•//magnetic.  A  ^magnetic  body,  on  the  other  hand,  when 
suspended  between  the  poles,  places  itself  equatorially,  that  is 
to  say,  places  its  length  at  right  angles  to  the  line  joining  the 
poles,  or,  more  generally,  tends  to  place  its  length  at  right  angles 
to  magnetic  lines  of  force. 

354.  Magnetic  Needles.  —  Any  magnet  suspended  at  the 
centre  so  as  to  turn  freely  is  called  a  magnetic  needle.  A 
common  form  of  the  needle  is  shown  in  the  upper  part  of 
Figure  309.  The  needle  may  be  suspended  so  as  to  turn 
in  a  horizontal  plane,  or  in  a  vertical  plane,  as  shown  in 


292 


NATURAL   PHILOSOPHY. 


Figure  310.     The  former  is  called  a  horizontal  needle,  and 
the  latter  a  dipping  needle. 


Fig.  309. 


Fig.  310. 


355.  Terrestrial  Magnetism.  —  If  a  steel  bar  is  exactly 
balanced  in  a  horizontal  position  in  the  frame  shown  in 
Figure  310,  which  is  suspended  by  a  thread  without  tor- 
sion, and  then  magnetized,  it  will  no  longer  remain  in  equi- 
librium in  any  position  in  which  it  may  be  placed,  but  it 
will  place  itself  in  a  particular  vertical  plane,  and  will  take 
a  particular  direction  in  this  plane.  The  magnetized  needle 
takes  this  particular  position  in  obedience  to  the  force  of 
terrestrial  magnetism.  The  earth  acts  upon  the  needle  as 
if  it  were  itself  a  magnet. 

The  vertical  plane  of  the  needle  is  called  the  magnetic 
meridian.  This  plane  usually  lies  several  degrees  from  a 
north  and  south  direction.  The  difference  between  true 
and  magnetic  north,  or  the  angle  between  the  geographical 
and  the  magnetic  meridian,  is  called  the  declination.  The 
direction  of  the  needle  in  the  vertical  plane  is  seldom  hori- 
zontal, but  inclined  by  a  greater  or  less  number  of  degrees 
to  the  horizon.  The  angle  which  the  needle  makes  with 
the  horizon  is  called  the  dip.  Both  the  declination  and 
the  dip  of  the  magnetic  needle  are  very  different  in  differ- 


NATURAL    PHILOSOPHY. 


2  93 


ent  parts  of  the  earth.     As  a  rule,  the  north  pole  of  the 
needle  dips  at  places  north  of  the  equator,  and  the  south 

Fig.  311. 


pole  at  places  south  of  the  equator.  In  the  neighborhood 
of  the  equator,  there  is  a  line  around  the  earth  on  which 
neither  pole  dips.  This  line  is  called  the  magnetic  equator. 


294  NATURAL    PHILOSOPHY. 

The  dip  increases  as  we  proceed  north  and  south  from  the 
magnetic  equator.  The  magnetic  meridians  and  lines  of 
equal  clip  are  shown  in  Figures  311  and  312.  It  will  be 
seen  that  the  magnetic  poles  are  at  some  distance  from  the 
geographic  poles.  The  magnetic  pole  north  of  the  equator 
is  a  south  magnetic  pole,  and  vice  versa. 

356.  Changes  in  the  Earth's  Magnetism.  —  The  earth's 
magnetism  appears  to  be  in  a  state  of  constant  fluctuation,  both 
as  regards  its  direction  and  its  intensity.  Some  of  these  varia- 
tions are  gradual,  and  extend  over  a  long  series  of  years ;  these 
changes  are  called  secular.  There  are  also  annual  and  diurnal 
variations,  which  seem  to  depend  upon  the  position  of  the  sun 
and  moon  with  respect  to  the  place  of  observation ;  but  over 
and  above  all  regular  and  periodic  changes,  there-  is  a  large 
amount  of  irregular  fluctuation,  which  occasionally  becomes  so 
great  as  to  constitute  what  is  called  a  magnetic  storm.  Mag- 
netic storms  are  not  connected  with  thunder-storms,  or  any 
other  known  disturbance  of  the  atmosphere  ;  but  they  are  inva- 
riably connected  with  exhibitions  of  aurora  borealis,  and  with 
spontaneous  galvanic  currents  in  the  ordinary  telegraph-wires  ; 
and  this  connection  is  found  to  be  so  certain  that,  upon  remark- 
ing the  display  of  one  of  the  three  classes  of  phenomena,  we  can 
at  once  assert  that  the  other  two  are  observable  (the  aurora 
borealis  sometimes  not  visible  here,  but  certainly  visible  in  a 
more  northern  latitude). 


NATURAL    PHILOSOPHY. 


295 


357.  Mariner's  Compass.  —  The  magnetic  action  of  the 
earth  has  received  its  most  important  application  in  the  mari- 
ner's compass.  This  is  a  declination  compass  used  in  guiding 
the  course  of  a  ship.  Figure  313  represents  a  view  of  the 
whole,  and  Figure  314  a  verti-  Fig  3,4 

cal  section.  It  consists  of  a 
cylindrical  case,  B  B1,  which, 
to  keep  the  compass  in  a 
horizontal  position  in  spite 
of  the  rolling  of  the  vessel,  is  supported  on  gimbals.  These  are 
two  concentric  rings,  one  of  which,  attached  to  the  case  itself, 
moves  about  the  axis  xd  which  plays  in  the  outer  ring  A  B ; 
and  this  moves  in  the  supports  P  Q,  about  the  axis  m  ti,  at  right 
angles  to  the  first.  In  the  bottom  of  the  box  is  a  pivot,  on 
which  is  placed,  by  means  of  an  agate  cap,  a  magnetic  bar  a  b, 
which  is  the  needle  of  the  compass.  On  this  is  fixed  a  disc  of 
mica,  a  little  larger  in  diameter  than  the  length  of  the  needle,  on 
which  is  traced  a  star  or  rose  with  thirty-two  branches,  making 
\\\&  points  of  the  compass  (Fig- 
ure 315).  The  branch  ending 
in  a  small  star  (Figure  313),  and 
marked  A',  is  in  a  line  with  the 
bar  ab,  which  is  underneath 
the  disc.  The  compass  is 
placed  near  the  stern  of  the 
vessel,  in  sight  of  the  helmsman. 
Knowing  the  direction  of  the 
compass  in  which  the  ship  is 
to  be  steered,  he  has  the  rudder 
turned  till  the  direction  coin- 
cides with  the  sight-vane  passing 
through  a  line  d  marked  on  the  inside  of  the  box,  and  parallel 
with  the  keel  of  the  vessel. 

Neither  the  inventor  of  the  compass  nor  the  exact  time  of  its 
invention  is  known. 


VI. 

ELECTRICITY. 

I. 
FRICTIONAL    ELECTRICITY. 

A.   ELECTRICAL  ATTRACTIONS  AND  REPULSIONS. 

358.  Electrical  Excitation.  —  If  a  dry  stick  of  sealing- 
wax  is  rubbed  with  a  piece  of  dry  flannel,  or  a  vulcanite 
tube  with  a  piece  of  dry  fur,  it  acquires  the  power  of  at- 
tracting light  bodies,  such  as  bits  of  paper,  pieces  of  straw, 
pith .  balls,  etc.  The  body  rubbed  is  said  to  be  electrified, 
and  the  force  which  it  manifests  is  called  electricity.  It 
has  been  found  that  electricity  is  developed  whenever  any 
two  unlike  bodies  are  rubbed  together,  though  some  bodies 
become  electrified  much  more  readily  than  others.  The 
ancients  noticed  that  amber,  which  the  Greeks  called  elec- 
tron, acquired  the  power  of  attracting  light  bodies  when 
rubbed  ;  hence  the  terms  electrified  and  electricity. 

Electricity  can  be  most  readily  and  conveniently  excited 
by  rubbing  a  smooth  vulcanite  tube,  18  inches  or  so  in 
length  and  ^  of  an  inch  in  diameter,  with  a  cat-skin  ;  or 
a  glass  tube  of  the  same  dimensions  with  a  silk  pad,  com- 
posed of  three  or  four  layers  of  silk,  and  8  or  10  inches 
square.  The  silk  pad  is  much  more  effective  when  covered 
with  amalgam,  a  mixture  of  i  part  by  weight  of  tin,  2  parts 
of  zinc,  and  6  of  mercury.  The  pad  should  be  first  smeared 
with  lard,  and  then  the  powdered  amalgam  sprinkled  over 


NATURAL    PHILOSOPHY. 


297 


it.     The  tubes  and  rubbers  work  better  when  they  are  dry 
and  hot. 

359.   Electrical  Attraction.  —  A  pith  ball  hung  on  a  silk 
thread  (Figure  316)  will  be  attracted  on  presenting  to  it 

Fig.  316.  Fig.  317. 


either  an  excited  glass  or  vulcanite  tube,  without  allowing 
it  to  touch  the  ball. 

A  long  straw,  mounted  so  as  to  turn  freely  on  a  needle 
stuck  into  a  rod  of  sealing-wax  (Figure  317),  may  be  at- 
tracted round  and  round  by  either  the  excited  glass  or 
vulcanite  rod. 

An  ordinary  walking-stick  placed  in  a  wire 
loop,  suspended  by  a  narrow  silk  ribbon 
(Figure  318),  may  be  pulled  around  by 
either  of  the  excited  tubes. 

Fig.  319- 


Fig.  31 


298  NATURAL   PHILOSOPHY. 

An  ordinary  lath  balanced  on  an  egg  in  an  egg-cup 
(Figure  319)  is  sensibly  attracted  by  the  glass  or  vulcanite 
tube  when  electrified. 

360.  Electrical  Repulsion.  —  Place  an  electrified  glass  tube 
in  the  loop  shown  in  Figure  318,  and  present  another  ex- 
cited glass  tube  to  it.  The  tube  in  the  loop  will  be  repelled. 
An  electrified  vulcanite  tube  placed  in  the  same  loop  will 
also  be  repelled  on  presenting  a  second  electrified  vulca- 
nite tube  to  it.  If  the  pith  ball  of  Figure  316  is  allowed 
to  touch  either  the  electrified  glass  or  vulcanite  tube,  it  will 
soon  be  repelled,  and  it  cannot  again  be  induced  to  touch 
the  tube  (Figure  320). 

361 .  Two  Kinds  of  Electricity.  —  If  an 
electrified  vulcanite  tube  is  placed  in 
the  wire  loop  of  Figure  318,  and  an  elec- 
trified glass  tube  be  presented  to  it,  the 
vulcanite  will  be  attracted  ;  while,  as  we 
have  seen,  it  will  be  repelled  on  present- 
ing an  electrified  vulcanite  tube  to  it. 
So,  also,  if  an  excited  glass  tube  is  placed 
in  the  loop,  it  will  be  repelled  by  an  ex- 
cited glass  tube,  but  attracted  by  an 
excited  vulcanite  tube. 
We  thus  see  that  there  are  two  kinds  of  electricity :  one 
appearing  on  glass  when  rubbed  with  silk,  and  the  other 
on  vulcanite  when  rubbed  with  fur.  The  former  is  called 
positive,  or  vitreous  electricity  ;  and  the  latter,  negative,  or 
resinous  electricity. 

When  bodies  are  electrified,  they  are  said  to  be  charged 
with  electricity.  Bodies  charged  with  like  electricities 
repel  each  other,  and  those  charged  with  unlike  electrici- 
ties attract  each  other. 

362.  Electrification  of  the  Rubber.  —  The  silk  pad  used 
in  exciting  the  glass  tube  becomes  negatively  electrified, 
and  the  cat-skin  used  in  exciting  the  vulcanite  tube  be- 


NATURAL    PHILOSOPHY.  299 

comes  positively  electrified.  This  may  be  shown  by  the 
following  experiments.  Hang  the  vulcanite  tube  in  the 
loop,  having  first  carefully,  discharged  the  tube  by  rubbing 
the  hand  over  it.  Protect  the  silk  pad  from  the  hand  with 
a  piece  of  thin  sheet-rubber.  Excite  the  glass  rod  with  the 
pad,  and  then  present  the  pad  to  the  vulcanite  tube.  It 
will  be  seen  to  attract  the  tube.  Charge  the  vulcanite 
tube  by  friction  with  the  cat-skin,  and  it  will  be  repelled 
by  the  pad  which  has  been  used  in  exciting  a  glass  tube, 
showing  that  the  pad  ^  negatively  electrified.  Similar 
experiments  may  be  tried  with  the  cat-skin  used  in  exciting 
the  vulcanite  tube.  Whenever  electricity  is  developed  by 
friction,  equal  quantities  of  both  kinds  of  electricity  are 
obtained,  one  on  the  body  rubbed  and  one  on  the  rubber. 

B.   ELECTRICAL  CONDUCTION  AND  INSULATION. 

363.  CottrelFs  Straw  Electroscope.  —  An  electroscope  is 
an  instrument  used  for  indicating  the  presence  of  elec- 
tricity, and,  also,  for  ascertaining  whether  the  electricity  is 
positive  or  negative.  The  straw  electroscope,  devised  by 
Mr.  Cottrell,  is  very  cheap  and  convenient.  It  consists 

Fig.  321. 


of  a  small  metallic  disc  M  (Figure  321),  supported  on  a 
rod  of  glass  or  sealing-wax  G,  and  of  a  smaller  disc  N,  of 
gilt-paper,  above  this,  fastened  with  sealing-wax  to  one  end 
of  a  long  straw  //',  capable  of  turning  upon  the  needle 
a  a'  as  an  axis.  The  disc  TV  is  balanced  by  a  little  piece  of 
bent  wire  at  /,  just  heavy  enough  to  separate  TV  from  M. 

364.    Conductors.  —  If   a   fine    copper   or  iron  wire   be 
fastened  to  the  disc  M  at  one  end,  and  coiled  around  the 


3°° 


NATURAL    PHILOSOPHY. 


glass  or  vulcanite  tube  at  the  other,  on  exciting  the  tube 
the  disc  N  is  at  once  attracted,  and  the  end  /  of  the  straw 
thrown  upward.  The  attraction  of  the  disc  N  shows  that 
the  electricity  excited  on  the  tube  has  passed  along  the 
wire  to  the  disc  M,  Substances  which  allow  electricity 
to  pass  through  them  are  called  conductors  of  electricity. 
The  metals,  charcoal,  acids,  rain-water,  linen,  plants,  and 
animals  are  conductors.  Alcohol,  dry  wood,  paper,  and 
straw  are  semi-conductors. 

365.  Insulators. —  If  the  disc  M  be  connected  with  the 
glass  or  vulcanite  tube  by  means  of  a  silk  thread,  the  disc 
N  will  not  be  attracted  on  exciting  the  tube.  This  shows 
that  electricity  will  not  pass  through  silk.  Substances 
through  which  electricity  will  not  pass  are  called  insulators. 
India-rubber,  vulcanite,  dry  paper,  hair,  silk,  glass,  wax, 
sulphur,  shellac,  and  dry  air  are  insulators. 

Conductors  are  said  to  be  insulated  when  they  are  com- 
pletely surrounded  by  insulators.  A  conductor  may  be 
insulated  by  hanging  it  on  a  silk  cord  or  ribbon,  or  by 
supporting  it  on  glass,  vulcanite,  or  sealing-wax. 

Fig.  322. 


ELECTRICAL  INDUCTION. 


366.  Electrical  Induction.  —  Balance  a  lath  upon  a  warm 
tumbler  or  short  rod  of  vulcanite  (Figure  322).  Place 
some  bits  of  paper  or  elder  pith  upon  a  stand  A,  three  or 


NATURAL    PHILOSOPHY.  301 

four  inches  below  the  end  Z  of  the  lath,  and  hold  an  ex- 
cited glass  or  vulcanite  tube  near  the  other  end  of  the  lath 
without  touching  it.  The  light  bodies  will  be  attracted, 
showing  that  the  lath  has  been  electrified.  Remove  the 
excited  tube  and  the  light  bodies  will  fall  away,  showing 
that  the  lath  has  again  become  neutralized.  In  this  case 
the  electrification  of  the  lath  took  place  through  the  air. 
This  development  of  electricity  by  a  charged  body  through 
an  insulating  medium  is  called  induction. 
Fig.  323. 


Connect  one  end  of  a  small  insulated  conductor  C 
(Figure  323)  by  means  of  a  wire  supported  by  silk  loops  to 
the  disc  M  of  Cottrell's  electroscope.  Bring  an  excited 
tube  near  the  conductor  without  touching  it,  the  disc  N  is 
immediately  attracted.  Remove  the  tube,  and  TV  is  again 
liberated.  If  you  touch  the  conductor  C  while  the  excited 
tube  is  held  near  it,  the  disc  N  is  promptly  liberated.  If 
now  you  remove  first  the  finger  and  then  the  tube,  the  disc 
will  again  be  attracted,  showing  that  the  conductor  and 
disc  are  now  permanently  charged.  In  this  case  the  body 
becomes  charged  by  induction. 

367.  The  Electrophorus.  —  The  electrophorus  consists  of 
a  plate  of  wax  or  vulcanite  (Figure  324),  and  of  a  lid  of 
tin  or  brass  with  an  insulating  handle.  Excite  the  plate 
by  stroking  it  with  a  cat-skin,  and  place  the  lid  upon  it. 


302 


NATURAL   PHILOSOPHY. 


Owing  to  the  unevenness  of  the  plate,  the  lid  will  touch  it 
at  comparatively  few  points,  but  the  plate  will  act  upon 
Fig.  324.  the  lid  by  induction.     Remove  the  lid, 

and  test  it  with  a  suspended  pith  ball 
(Figure  316).  It  shows  no  signs  of 
electrification.  Replace  the  lid  and 
touch  it  with  the  finger.  Remove  the 
finger  and  then  the  lid,  and  present  the 
lid  to  the  pith  ball.  The  ball  is  at- 
tracted, showing  that  the  lid  is  charged. 
Allow  the  pith  ball  to  touch  the  lid.  It 
kis  immediately  repelled,  having  by  contact  become  charged 
with  the  same  kind  of  electricity  as  that  on  the  lid.  Pre- 
sent now  the  plate  of  the  electrophorus  to  the  charged 
pith  ball,  and  the  ball  will  be  attracted,  showing  that  the 
lid  was  charged  with  the  opposite  electricity  to  that  on  the 
plate.  Bodies  charged  by  contact  are  always  charged  with 
the  same  electricity  as  that  on 
the  body  acting  upon  them,  while 
bodies  charged  by  induction  are 
always  charged  with  the  oppo- 
site electricity  to  that  on  the 
body  acting  upon  them.  The 
lid  of  the  electrophorus  may 
be  charged  any  number  of 
times  by  the  plate  without  re- 
newing the  charge  on  the 
plate. 

3  68 .  Gold- Leaf  Electroscope. 
—  This  instrument  (Figure 
325)  consists  of  two  strips  of 
gold  leaf,  which  in  a  large 
instrument  may  be  4  inches 
long  and  i  inch  wide,  hung 
together  by  their  upper  ends 


Fig.  325- 


NATURAL    PHILOSOPHY.  303 

to  a  metal  rod.  This  rod  passes  through  a  hole  in  the  top 
of  a  glass  shade,  inside  of  which  the  gold  leaves  hang. 
The  rod  terminates  above  in  a  brass  disc  or  a  brass  ball. 
The  glass  shade  serves  at  once  to  insulate  the  disc  and 
leaves,  and  to  protect  the  leaves  from  currents  of  air. 

When  an  electrified  body  is  placed  in  contact  with  the 
disc,  it  charges  the  disc  and  leaves  with  its  own  electricity, 
and  causes  the  leaves  to  diverge.  Owing  to  the  lightness 
of  the  gold  leaves,  this  is  a  very  sensitive  instrument  for 
detecting  the  presence  of  small  quantities  of  electricity. 

To  detect  the  kind  of  electricity  on  the  charged  body, 
first  charge  the  leaves  with  a  known  kind  of  electricity,  and 
then  place  the  body  to  be  tested  in  contact  with  the  disc. 
If  the  leaves  diverge  mere  than  before,  the  body  is  charged 
with  the  same  kind  of  electricity  as  that  on  the  leaves  ;  if 
the  leaves  diverge  less  than  before,  the  body  is  charged 
with  the  opposite  electricity  to  that  on  the  leaves. 

If  a  charged  body  is  brought  near  the  disc  without 
touching  it,  the  leaves  will  diverge,  being  electrified  by 
induction.  Remove  the  charged  body,  and  the  leaves 
come  together  again.  If  we  present  the  charged  body 
again,  and  touch  the  disc  with  the  finger,  the  leaves  fall 
together.  Remove  first  the  finger  and  then  the  charged 
body,  and  the  leaves  again  diverge,  being  charged  by 
induction  with  the  opposite  electricity  to  that  on  the 
charged  body. 

369.  Electric  Carrier.  —  The  proof  plane  is  often  em- 
ployed in  transferring  electricity  from  a  charged  body  to 
an  electroscope.  It  consists  of  a  metallic  disc  about  2 
inches  in  diameter  with  an  insulating  handle.  If  we  touch 
a  charged  body  with  the  disc,  it  takes  off  some  of  the 
electricity  from  the  part  touched.  The  electricity  on  the 
proof  plane  may  then  be  tested  by  an  electroscope.  A 
cheap  and  convenient  electric  carrier  may  be  made  by 
fastening  a  bit  of  tin-foil  2  or  3  inches  square  to  one  end 


304  NATURAL    PHILOSOPHY. 

of  a  vulcanite  rod  8  or  10  inches  long,  as  shown  in  Figure 
Fig.  326.  326.  The  tin-foil  may  be  stuck  to  the  rod  with 
sealing-wax.  The  stem  of  the  carrier  in  the  fig- 
ure is  a  straw  stuck  to  a  rod  of  sealing-wax  as  a 
handle. 

370.  Two  Kinds  of  Electricity  developed  in  In- 
duction. —  Charge  the  lid  of  the  electrophorus, 
and  hold  it  near  one  end  of  an  insulated  con- 
ductor. Place  the  carrier  in  contact  with  the  lid, 
and  then  with  the  disc  of  the  gold-leaf  electro- 
scope, so  as  to  charge  the  leaves  with  the  elec- 
tricity on  the  lid.  Discharge  the  carrier,  and 
bring  it  in  contact  with  the  "far  end"  of  the  insulated 
conductor.  Again  place  the  carrier  on  the  disc  of  the 
electroscope ;  the  leaves  will  diverge  more  than  before, 
showing  that  the  far  end  of  the  conductor  has  upon  it  the 
same  electricity  as  the  inducing  lid.  Again  discharge  the 
carrier,  and  bring  it  in  contact  with  the  "  near  end  "  of 
the  conductor.  Remove  the  carrier  again  to  the  disc 
of  the  electroscope ;  the  leaves  will  diverge  less  than 
before,  showing  that  the  near  end  of  the  conductor  has  the 
opposite  kind  of  electricity  to  that  on  the  lid.  In  a  simi- 
lar way,  the  centre  of  the  conductor  will  be  found  to  be 
neutral.  Both  kinds  of  electricity  are  always  developed  in 

Fig.  327. 


€ 


induction  ;  the  same  kind  of  electricity  as  that  on  the 
inducing  body  being  driven  to  the  far  end  of  the  conductor, 
and  the  opposite  kind  being  held  on  the  near  end  of  the 
conductor  (Figure  327). 

While  the  opposite  electricity  to  that  on  the  inducing 
body  is  held  fast  by  the  inducing  body,  the  other  elec- 


NATURAL   PHILOSOPHY. 


305 


tricity  is  driven  off  to  the  farthest  possible  point.  If  two 
insulated  conductors  are  connected  by  a  long  wire,  and  the 
lid  of  the  electrophorus  is  presented  to  one  of  them, 
the  near  conductor  becomes  charged  with  negative  elec- 
tricity and  the  far  conductor  with  positive  electricity.  If 
we  touch  a  conductor  under  the  influence  of  a  charged 
body,  or  connect  the  conductor  in  any  way  with  the  earth, 
the  far  end  of  the  conductor  becomes  the  opposite  side  of 
the  earth,  to  which  the  electricity  like  that  on  the  inducing 
body  is  driven.  Hence,  when  bodies  connected  with  the 
earth  are  acted  on  by  induction,  they  have  only  one  kind 
of  electricity  on  them,  and  that  the  opposite  to  that  on  the 
inducing  body.  Hence  bodies  when  charged  by  induction 
always  become  charged  with  the  opposite  electricity  to  that 
on  the  inducing  body.  In  charging  a  conductor  by  induc- 
tion it  is  necessary  to  remove  the  earth  connection  before 
removing  the  inducing  body,  else  the  electricity  which  was 
held  fast  on  the  conductor  would  escape  to  the  earth  to 
join  the  electricity  which  had  been  driven  there  before  it. 

371.  Quantity  of  Electricity  developed  by  Induction. — 
Every  charged  body  develops  on  surrounding  bodies  equal 
quantities  of  opposite  electricities,  and  an  amount  of  each  elec- 
tricity equal  to  that  on  the  charged  body. 

Suspend  an  ordinary  tea-canister  by  a  white  silk  cord  and 
connect  it  by  a  wire  with  an  electroscope.  Lower  a  metallic 
ball  hung  on  a  silk  thread  and  charged  with  electricity  into  the 
canister  without  touching  it.  The  inductive  action  of  the  ball 
will  be  wholly  on  the  canister  in  which  it  is  enclosed.  It  will 
drive  its  own  kind  of  electricity  to  the  outside  of  the  canister, 
and  hold  the  opposite  electricity  on  the  inside.  The  leaves  of 
the  electroscope  will  be  made  to  diverge  by  the  electricity  sent 
to  the  outside.  Remove  the  ball  from  the  canister  without  its 
having  touched  it.  The  gold  leaves  will  fall  together,  showing 
that  the  canister  has  lost  all  trace  of  electricity.  The  two  kinds 
of  electricity  developed  by  the  induction  of  the  ball  must  have 
been  exactly  equal,  since  they  neutralize  each  other  on  reuniting. 


306  NATURAL    PHILOSOPHY. 

Again  lower  the  charged  ball  into  the  canister  without 
touching  it,  and  touch  the  outside  of  the  canister  with  the  fin- 
ger, so  as  to  allow  the  electricity  on  it  to  pass  to  the  earth.  The 
canister  is  now  charged  with  the  electricity  held  on  the  inside 
by  the  ball.  Remove  the  finger  and  allow  the  ball  to  touch  the 
inside  of  the  canister,  and  then  remove  it.  Neither  the  ball  nor 
the  canister  will  show  any  trace  of  electricity.  The  electricity 
on  the  ball  has  exactly  neutralized  that  on  the  inside  of  the 
canister.  Hence  they  must  have  been  equal  in  amount.  The 
electricity  on  the  outside  of  the  canister  has  already  been  shown 
equal  to  that  on  the  inside ;  hence  each  is  equal  to  that  on  the 
ball. 

372.  Dielectrics.  —  Induction  will  take  place  through  all 
insulating  substances.  When  an  excited  tube  is  brought 
near  the  disc  of  the  electroscope,  the  leaves  diverge  be- 
cause of  the  induction  which  takes  place  through  the  air. 
If  a  plate  of  glass,  of  vulcanite,  of  paraffin,  or  of  shellac, 
is  held  between  the  tube  and  the  disc,  the  leaves  will  still 
diverge  because  of  the  induction  which  is  taking  place 
through  the  plate.  The  substance  through  which  induc- 
tion takes  place  is  called  a  dielectric.  All  insulators  are 
dielectrics. 

If  a  metallic  plate,  large  enough  so  that  induction  will 
not  take  place  around  it,  is  held  between  the  tube  and  the 
disc  of  the  electroscope,  so  as  to  be  in  connection  with 
the  earth,  the  leaves  of  the  electroscope  will  no  longer 
diverge.  No  induction  will  take  place  through  such  a 
conductor.  If  the  conducting  plate  were  insulated,  induc- 
tion would  appear  to  take  place  through  it,  because  elec- 
tricity would  be  developed  on  the  far  side  of  the  plate  by 
induction,  and  this  electricity  would  carry  on  induction 
through  the  air. 

Some  dielectrics  allow  induction  to  take  place  through 
them  more  readily  than  others.  These  are  said  to  have 
greater  specific  inductive  capacities  than  the  others,  that  is 
to  say,  greater  capacities  for  carrying  on  induction.  The 


NATURAL    PHILOSOPHY.  307 

comparative  inductive  capacity  of  different  insulators  has 
been  much  studied  in  recent  times,  owing  to  its  great  prac- 
tical importance  in  submarine  telegraphy. 

The  inductive  action  between  two  conductors  depends 
upon  the  distance  the  conductors  are  apart  and  upon  the 
specific  inductive  capacity  of  the  intervening  insulator. 
The  less  the  distance  and  the  greater  the  specific  inductive 
capacity  of  the  insulator,  the  more  powerful  the  inductive 
action. 

373.  "Condition  of  the  Dielectric  during  Induction.  —  When 
a  body  becomes  charged  its  electricity  tends  to  escape  to  sur- 
rounding bodies.  If  it  be  connected  to  any  of  these  bodies  with 
a  metallic  wire,  the  electricity  will  flow  through  this  wire  just  as 
water  will  flow  through  a  pipe.  When  the  charged  body  is 
connected  to  a  neighboring  body,  the  electricity  in  its  attempt 
to  pass  to  the  body  through  the  dielectric  throws  the  dielectric 
into  a  state  of  strain.  Suppose  a  pipe  full  of  water  to  be  crossed 
at  short  intervals  with  elastic  partitions.  Should  we  attempt  to 
force  water  through  such  a  pipe,  the  partitions  would  be  bent 
forward  one  after  another  ;  that  is  to  say,  a  state  of  strain  would 
be  propagated  through  the  pipe,  and  this  state  of  strain  would 
continue  as  long  as  there  was  an  attempt  to  force  water  through 
the  pipe.  In  some  such  way  a  dielectric  seems  to  be  thrown 
into  a  state  of  strain  by  the  attempt  of  the  electricity  to  pass 
through  it  This  state  of  strain  appears  to  be  propagated 
through  an  insulator  with  the  velocity  of  light. 

3  74.  Attraction  and  Repulsion  of  Light  Bodies.  —  We  now 
see  why  a  charged  body  attracts  a  light  body  not  pre- 
viously charged.  It  first  acts  upon  the  light  body  by 
induction,  inducing  a  change  similar  to  its  own  on  the  far 
side  of  the  body  and  an  opposite 
change  on  the  near  side  (Figure  328). 
The  near  side  is  attracted  and  the 
far  side  repelled  ;  but  the  attracted 
side  being  nearer,  the  attraction  is 
stronger  than  the  repulsion,  and  the 


308  NATURAL    PHILOSOPHY. 

body  as  a  whole  is  attracted.  On  touching  the  charged 
body  it  gives  up  to  it  the  electricity  on  its  near  side,  and  so 
becomes  charged  with  the  same  electricity  as  that  on  the 
charged  body,  and  is  then  repelled. 

D.   ELECTRICAL  POTENTIAL. 

375.  Potential.  —  The  tern*,  potential  in  Physics  means 
condition  as  regards  work.     The  potential  of  a  point  with 
respect  to  a  force  is  the  condition  of  the  point  as  regards 
work  done  by  that  force.     Thus  the  gravitation  potential 
of  a  point  is  the  condition  of  that  point  as  regards  work 
done  by  gravity ;  and  the  electrical  potential  of  a  point  is 
its  condition  as  regards  work  done  by  electricity. 

376.  Gravitation  Potential.  —  The  absolute  gravitation  po- 
tential of  a  point  is  measured  by  the  amount  of  work  that  would 
be  done  by  gravity  in  impeding  the  motion  of  a  unit  of  mass,  as 
the  mass  is  moved  from  a  point  to  an  infinite  distance,  or  in 
aiding  its  motion,  as  the  mass  is  moved  from  an  infinite  dis- 
tance up  to  the  point.     Thus,  when  we   say  that  the  absolute 
gravitation  potential  of  a  point  is  50,000,  we  mean  that  the  con- 
dition of  a  point  is  such  that  50,000  units  of  work  would  be  done 
by  gravity  in  impeding  the  motion  of  a  unit  of  mass  if  it  were 
moved  from  that  point  to  an  infinite  distance,  or  in  aiding  the 
motion  of  the  mass  if  it  were  moved  from  an  infinite  distance  to 
the  point. 

The  difference  in  gravitation  potential  between  two  points  is 
measured  by  the  amount  of  work  that  would  be  done  by  gravity 
upon  a  unit  of  mass,  in  aiding  or  impeding  its  motion,  were  it 
moved  from  one  point  to  the  other.  Thus,  when  we  say  that 
the  difference  of  gravitation  potential  between  two  points  is  40, 
we  mean  that  the  two  points  are  in  such  condition  that,  were 
a  unit  of  mass  moved  from  one  point  to  the  other,  40  units  of 
work  would  be  done  upon  it  by  gravity  in  aiding  or  impeding  its 
motion.  Gravity  always  tends  to  move  a  body  from  a  lower 
potential  to  a  higher  one.  When  two  points  are  at  the  same 
gravitation  potential,  no  work  would  be  done  by  gravity  upon  a 


NATURAL   PHILOSOPHY.  309 

body  in  its  motion  from  one  point  to  the  other,  because  gravity 
would  have  no  tendency  to  aid  or  impede  its  motion.  Two 
points  at  the  same  gravitation  potential  are  said  to  be  at  the 
same  level.  The  term  level  is  ordinarily  used  with  gravity  for 
potential,  but  a  high  level  corresponds  to  a  low  potential. 

377.  Electrical  Potential.  —  The  absolute  electrical  potential 
of  a  point  is  measured  by  the  amount  of  work  that  would  be 
done  by  electricity  in  aiding  or  impeding  the  motion  of  a  small 
body  charged  with  a  unit  of  electricity,  were  the  body  moved 
from  the  point  to  an  infinite  distance,  or  from  an  infinite  distance 
to  the  point.  When  we  say  that  the  absolute  electrical  poten- 
tial of  a  point  is  90,  we  mean  that  the  condition  of  the  point  is 
such  that  90  units  of  work  would  be  done  by  electricity  upon  a 
small  body  charged  with  a  unit  of  electricity  in  aiding  or  im- 
peding its  motion,  were  it  moved  from  the  point  to  an  infinite 
distance,  or  from  an  infinite  distance  to  the  point.  The  C.  G.  S. 
unit  of  electricity  is  the  amount  of  electricity  that  would  exert  a 
dyne  offeree  at  the  distance  of  a  centimetre. 

The  difference  of  electrical  potential  between  two  points  is 
measured  by  the  amount  of  work  that  would  be  done  by  elec- 
tricity upon  a  small  body  charged  with  a  unit  of  electricity  in 
aiding  or  impeding  its  motion,  were  it  moved  from  one  point  to 
the  other.  When  we  say  that  the  difference  in  electrical  poten- 
tial between  two  points  is  15,  we  mean  that  the  points  are  in 
such  conditions  that  15  units  of  work  will  be  done  by  electricity 
in  aiding  or  impeding  the  motion  of  a  small  body  charged  with 
a  unit  of  electricity,  were  it  moved  from  one  point  to  the  other. 

Electricity  always  tends  to  move  a  body  charged  with 
positive  electricity  from  a  higher  to  a  lower  potential. 

When  two  points  are  at  the  same  electrical  potential, 
electricity  does  not  tend  to  move  a  charged  body  from 
either  point  to  the  other,  and  consequently  no  work  would 
be  done  by  electricity  upon  a  charged  body  in  its  motion 
from  one  point  to  the  other. 

When  the  term  potential  is  used  without  qualification,  it 
is  always  understood  to  mean  electrical  potential.  Poten- 
tial for  electricity  corresponds  to  level  for  gravity.  A  sur- 


310  NATURAL    PHILOSOPHY. 

face  all  of  whose  points  are  at  the  same  potential  is  called 
an  equipotential  surface.  It  corresponds  to  a  level  surface. 
As  gravity  never  tends  to  produce  motion  along  a  level  sur- 
face, so  electricity  never  tends  to  produce  motion  along  an 
equipotential  surface.  As  gravity  acts  perpendicularly  at 
every  point  to  a  level  surface,  so  electricity  acts  perpendicu- 
larly at  every  point  to  an  equipotential  surface. 

In  electricity,  the  potential  of  the  earth  is  taken  as  zero, 
and  the  potential  of  a  point  is  really  the  difference  between 
its  potential  and  that  of  the  earth.  Electrical  potential  is 
usually  defined  in  terms  of  positive  electricity.  A  positive 
potential  is  one  higher  than  that  of  the  earth,  and  a  nega- 
tive potential  is  one  lower  than  that  of  the  earth. 

378.    Electrometers.  —  An  electroscope  is  an  instrument  for 
detecting  the  presence  of  electricity,  and  for  ascertaining 
Fig.  329.    its  quality.     An  electrometer  is  an  instrument  for 
measuring  the  intensity  of   electrical  attraction 
and  repulsion,  and  for  ascertaining  the  poten- 
tial of  a  body. 

379.  Pith-ball  Electrometer. — The  pith-ball  elec- 
trometer is  shown  in  Figure  329.  A  wooden  stem 
C  is  mounted  in  a  metallic  socket,  which  can 
be  screwed  to  the  conductor  whose  electrifica- 
tion is  to  be  measured.  A  pith  ball  fixed  to  a 
straw  stem  A  hangs  from  a  pivot  at  the  centre  of 
the  divided  arc  B.  Electricity  is  communicated 
from  the  metal  socket  to  the  ball,  which  is  repelled.  The 
number  of  degrees  over  which  the  straw  passes  indicates 
roughly  the  strength  of  the  electrification  of  the  conductor. 

380.  Coulomb's  Torsion  Balance.  —  This  instrument  is  shown 
in  Figure  330.  A  long,  fine  thread  is  suspended  in  a  vertical 
tube.  The  thread  is  attached  at  the  top  to  a  rod  which  passes 
through  the  centre  of  a  horizontal  circle  called  the  torsion  cir- 
cle, which  is  divided  into  degrees,  and  can  be  turned  by  the  rod 
which  holds  the  thread.  A  pointer  on  the  tube  indicates  the 


NATURAL    PHILOSOPHY. 


number  of  degrees  the  circle  is  turned.  To  the  bottom  of  the 
thread  is  fastened  a  light  rod,  so  as  to  hang  horizontally.  The 
rod  carries  a  gilt  pith  ball  at  one  end,  and  a  similar  ball  at  the 
other  end  to  balance  it.  The  vertical  tube  in  which  the  thread 
is  suspended  stands  on  the  centre  of  a  horizontal  glass  plate, 

Fig.  33°- 


which  forms  the  lid  of  the  lower  part  of  the  case  in  which  the 
horizontal  arm  swings.  Another  gilt  pith  ball  of  the  same  size 
as  the  one  on  the  horizontal  arm  is  fixed  to  a  vertical  stem,  which 
passes  through  the  top  plate,  so  that  the  two  balls  may  be  brought 
into  contact.  A  circle  divided  into  degrees  is  engraved  on  the 
lid  of  the  lower  case,  and  the  base  of  the  case  is  a  looking-glass. 


312  NATURAL    PHILOSOPHY. 

To  use  the  instrument,  the  fixed  pith  ball  is  removed,  and  the 
torsion  circle  turned  till  the  suspended  pith  ball  occupies  exactly 
the  position  formerly  occupied  by  the  fixed  one.  When  it  has 
come  to  rest  in  this  position  there  is  no  torsion,  and  the  reading 
of  the  torsion  circle  is  taken  as  the  zero.  The  fixed  pith  ball  is 
then  electrified  and  put  in  position,  pushing  the  suspended  ball 
to  one  side,  and  at  the  same  time  communicating  half  its  charge  to 
it.  The  balls  now  repel  each  other,  and  if  the  length  and  thick- 
ness of  the  thread  and  the  strength  of  the  charge  have  been 
properly  adjusted,  the  suspended  arm  should  turn  through  from 
30°  to  45°.  The  position  of  the  straw  is  noted,  and  the  torsion 
circle  is  turned  so  as  to  force  the  balls  towards  each  other,  until 
the  straw  pointer  has  moved  through  an  angle  equal  to  one  di- 
vision of  the  engraved  circle.  The  number  of  degrees  through 
which  the  torsion  circle  has  been  turned  is  then  noted,  and  the 
process  is  repeated  for  several  divisions,  until  the  balls  are  forced 
rather  near  together.  A  table  can  then  be  formed,  showing  the 
force  of  repulsion  corresponding  to  each  decrement  of  distance, 
for  the  force  overcome  in  each  case  is  simply  proportional  to  the 
number  of  degrees  through  which  the  torsion  circle  has  been 
turned. 

A  slight  modification  of  the  arrangements  will  enable  the  force 
of  attraction  to  be  measured  when  the  two  balls  are  oppositely 
electrified. 

By  means  of  this  instrument,  Coulomb  ascertained  that  the 
force  of  attraction  or  repulsion  between  two  electrified  bodies, 
whose  sizes  are  very  small  compared  with  their  distance  apart, 
is  inversely  proportional  to  the  square  of  their  distances  apart; 
and  directly  proportional  to  the  product  of  their  changes. 

381.  Thomson's  Quadrant  Electrometer.  —  Thomson's  quad- 
rant electrometer  is  the  most  delicate  and  accurate  instru- 
ment that  has  been  devised  for  measuring  potential.  Figure  331 
serves  to  show  the  principle  on  which  this  instrument  is  con- 
structed. N  N\?,  a  light  needle  of  aluminium,  suspended  so  as 
to  be  able  to  turn  in  a  horizontal  plane.  This  needle  is  kept 
charged  to  a  constant  potential  by  being  connected  with  a  uni- 
form source  of  electricity.  Just  below  the  needle  are  four 
metallic  quadrants  placed  horizontally,  as  shown  in  Figure  332. 
Each  is  insulated  from  the  one  next  to  it,  but  connected  with  the 


NATURAL    PHILOSOPHY. 
Fig.  331.  Fig.  332. 


flow  from   the  charged   con- 


one   diagonally  opposite,   as 
shown  in  Figure  331. 

Suppose  the  needle  charged 
with  positive  electricity,  the 
unshaded  quadrant  connected 
to  earth,  and  the  shaded  ones, 
by  means  of  the  wire  b  (Fig- 
ure 331),  with  the  conductor 
whose  electrification  is  to 
be  measured.  Electricity  v 
ductor  to  the  shaded  quadrant  till  they  are  of  the  same  poten- 
tial as  itself.  The  direction  in  which  the  needle  is  deflected 
will  show  whether  the  conductor  is  charged  with  positive  or 
negative  electricity.  For  if  the  needle  is  deflected  to  the  right, 
it  must  be  because  it  is.  attracted  by  the  shaded  quadrants, 
that  is,  because  they  are  charged  negatively.  If  the  needle  is 
deflected  to  the  left,  it  must  be  because  these  quadrants  are 
charged  positively,  so  as  to  repel  the  needle.  The  potential  of 
the  conductor  is  indicated  by  the  amount  of  the  deflection  of  the 
needle.  The  greater  the  deflection  of  the  needle  the  higher  the 
potential  of  the  conductor,  and  the  less  the  deflection  the  lower 
the  potential. 

This  apparatus  may  be  used  for  adjusting  two  potentials  to 
equality.  If  two  similarly  electrified  bodies  are  connected  with 
the  shaded  and  unshaded  quadrants  respectively,  they  will  tend 
to  turn  the  needle  opposite  ways,  and  the  deflection  will  depend 
upon  the  difference  of  potential.  If  now  one  of  the  electrifica- 
tions be  varied  till  there  is  no  deflection,  we  shall  know  that  the 
potentials  have  been  brought  to  exact  equality. 

The  form  of  the  instrument  shown  in  Figure  332  is  only  a  lec- 
ture model.  The  inverted  vessel  at  the  top,  from  the  interior  of 
which  the  needle  is  suspended,  U  a  Lcyden  jar  for  maintaining  a 


NATURAL   PHILOSOPHY. 


constant  charge  on  the  needle.     The  action  of  this  jar  will  be 
described  farther  on. 

The  simplest  form  of  the  instrument  that  is  used  for  real  work 
is  known  as  the  Elliott  pattern.     It  is  shown  in  Figure  333.     It 
Fig.  333.  differs  from  the  lecture  model  in  that 

its  metal  quadrants  are  quarters,  not 
of  a  disc,  but  of  a  kind  of  "  pill-box," 
inside  which  the  needle  hangs.  Both 
sides  of  the  needle  are  thus  acted 
upon.  The  Leyden  jar  is  placed  at 
the  bottom  of  the  instrument.  It 
contains  strong  sulphuric  acid,  and 
the  connection  between  it  and  the 
needle  is  made  by  a  platinum  wire 
attached  to  the  needle,  and  dipping 
into  the  acid.  The  acid,  by  its  affin- 
ity for  moisture,  keeps  the  inside  of 
the  apparatus  always  dry.  Three 
metal  rods  project  from  the  instrument.  Two  (seen  on  the 
right)  are  connected  respectively  to  the  two  pairs  of  quadrants, 
and  the  third  (seen  in  the  front  of  the  figure)  can  be  connected 
to  the  needle  when  it  is  desired  to  charge  it  with  electricity.  The 
needle  is  suspended  by  what  is  called  a  "  bifilar  suspension,"  — 
that  is,  it  is  hung  by  two  fine  silk  threads,  side  by  side,  and  about 
-fa  of  an  inch  apart.  After  the  needle  has  been  displaced  from 
its  position  of  rest,  these  threads  always  tend  to  bring  it  back. 
The  position  of  the  needle  can  be  adjusted  by  turning  the  head 
at  the  top  of  the  glass  case  to  which  the  threads  are  attached. 

The  instrument,  when  in  use,  is  covered  by  a  wire  cage  con- 
nected to  earth,  to  protect  the  quadrants  from  the  induction  of 
neighboring  charged  bodies. 

E.   ELECTRICAL  CHARGE. 

382.  The  Charge  entirely  on  the  Surface.  —  Suspend  a  tea- 
canister  by  a  silk  cord,  and  charge  it  as  highly  as  possible 
by  means  of  the  electrophorus  or  other  electrical  machine. 
Lower  a  brass  ball  hung  on  a  silk  thread  into  it,  so  as  to 
touch  the  interior,  and  then  remove  it  without  touching  the 


NATURAL    PHILOSOPHY. 


315 


mouth  of  the  canister.  Test  the  ball  with  an  electroscope, 
and  it  will  be  found  to  have  brought  away  no  electricity  from 
the  can.  Bring  the  ball  in  contact  with  the  outside  of  the 
canister  and  present  it  to  the  electroscope,  and  it  will  be 
found  to  have  taken  electricity  away  from  the  canister.  By 
no  means  can  any  electricity  be  found  on  the  inside  of  a 
hollow  conductor.  Hence  we  conclude  that  the  charge  re- 
sides entirely  on  the  surface ;  unless,  of  course,  a  charge  is 
developed  on  the  inside  of  the  hollow  conductor  by  the 
induction  of  a  charged  body  suspended  within  it. 

Fig-  334-  Fig.  335. 


Fig.  336. 


Fig.  337- 


383.  Distribution  of  Electricity  over  the  Surface  of  a  Charged 
Body.  —  Were  a  spherical  conductor  suspended  on  a  silk 
thread  in  the  centre  of  a  large  room,  and  charged  with  elec- 
tricity, the  charge  would  be  distributed  uniformly  over  the 
surface,  as  shown  by  the  dotted  line  in  Figure  334.  The 

Fig.  338- 


dotted  lines  in  Figures  335, 336,  and  337  show  the  distribu- 
tion of  electricity  over  the  surface  of  an  ellipsoid,  a  cylinder 
with  rounded  ends,  and  a  disc  under  similar  circumstances. 
When  the  conductor  is  oblong,  the  electricity  tends  to  accu- 
mulate at  the  ends.  The  longer  and  thinner  the  con- 


316  NATURAL    PHILOSOPHY. 

ductor,  the  greater  the  accumulation  at  the  ends.  Figure 
338  shows  the  distribution  of  electric  charge  over  the  sur- 
face of  a  conductor  in  the  form  of  a  double  cone.  The 
numbers  indicate  the  intensities  of  the  charge  at  different 
points. 

384.  Density  of  the  Charge.  —  The  intensity  of  the  elec- 
trification at   any  point   on  a  body  is  called  the  electric 
density  at  that  point.     The  charge  of  a  body  is  the  quantity 
of  electricity  on  it.     The  density  at  a  point  of  surface,  when 
the  density  is  uniform,  is  the  amount  of  electricity  on  a 
square  centimetre  of  surface.      When  the  density  is  not 
uniform,  the  density  at  any  point  is  the  amount  of  electri- 
city that  there  would  be  on  a  square  centimetre  of  surface, 
were  its  electricity  everywhere  that  of  the  point. 

The  force  with  which  electricity  endeavors  to  escape 
from  any  portion  of  surface  increases  with  the  density  at 
that  point. 

The  density  at  different  points  of  the  surface  of  a  charged 
conductor  may  be  ascertained  by  applying  the  proof  plane 
to  different  portions  of  the  surface,  and  seeing  how  much 
electricity  it  carries  off  with  it.  The  density  on  different 
parts  of  the  surface  depends  upon  the  form  of  the  con- 
ductor and  the  influence  of  surrounding  bodies.  The  po- 
tential of  a  charged  conductor  must  be  the  same  at  every 
point  of  the  surface,  else  the  electricity  would  not  be  in  a 
state  of  equilibrium,  for  a  difference  of  potential  would 
tend  to  move  the  electricity  from  one  point  of  the  surface 
to  another.  The  potential  of  a  body  is  independent  of  the 
density  of  its  charge. 

385.  Tendency  of  Electricity  to  escape  from  Points.  —  Let 
M P N  (Figure  339)  be  a  section  of  a  pointed  charged  con- 
ductor, and  let  us  consider  the  forces  tending  respectively  to 
drive  off  a  unit  of   electricity  from  6"  on  the  side  of  the  con- 
ductor, and  from  P  on  its  point.     None  of  the  electricity  on 
M  P  can  act  upon  S  so  as  to  tend  to  cause  it  to  escape  from  the 


NATURAL    PHILOSOPHY.  317 

surface.  This  electricity  can  act  on  S  only  to  urge  it  to  the 
right  or  left  along  the  surface.  Only  such  portions  of  the  elec- 
tricity on  the  side  NP  as  are  moderately  near  S  would  tend  to 
separate  it  from  the  conductor.  None  of  the  electricity  on  this 
side  is  nearer  than  3  to  S,  and  only  the  portion  A  B  is  nearer 
than  4.  Now,  as  the  force  of  repulsion  decreases  as  the  square 

Fig.  339- 


of  the  distance  increases,  and  as  a  good  deal  of  the  electricity 
between  //  and  B  acts  upon  S  obliquely  to  the  surface  M  P,  the 
component  of  the  repulsion  acting  upon  ^perpendicularly  to  the 
surface  would  be  very  small.  When  we  consider  the  whole  con- 
ductor instead  of  the  section,  the  nearer  we  come  to  S  the  more 
obliquely  the  repulsive  force  acts  upon  it,  and  the  weaker  the 
perpendicular  component  Upon  P,  on  the  contrary,  there  is 
electricity  acting  at  all  the  distances  from  o  up  to  4,  and  it  is  all 
acting  very  nearly  in  the  direction  that  would  tend  to  drive  the 
electricity  off  from  the  point,  as  is  indicated  by  the  arrows.  And 
this  is  still  the  case,  whether  we  consider  the  whole  conductor 
or  its  section.  Hence  there  is  a  much  greater  tendency  to  drive 
electricity  off  from  a  point  than  from  any  other  part  of  a 
conductor. 

If  a  sharp  metallic  point  is  fixed  to  one  end  of  a  small 
insulated  conductor,  and  the  lid  of  the  electrophorus 
charged  with  positive  electricity  is  held  in  front  of  the 
point  so  as  to  act  upon  the  conductor  by  induction,  nega- 
tive electricity  will  escape  from  the  point  to  the  lid,  and  on 
removing  the  lid  the  conductor  will  be  found  to  be  charged 
feebly  with  positive  electricity.  If  the  charged  lid  of  the 
electrophorus  is  held  near  the  other  end  of  the  conductor, 
positive  electricity  will  escape  from  the  point,  and  on  re- 
moving the  lid  the  conductor  will  be  found  to  be  charged 
feebly  with  negative  electricity.  If  a  plate  of  dry  glass  is 


318  NATURAL    PHILOSOPHY. 

held  between  the  lid  of  the  electrophorus  and  the  point, 
negative  electricity  will  escape  from  the  point  to  the  glass, 
which  will  be  found  on  examination,  after  removal,  to  be 
charged  with  negative  electricity. 

Charged  conductors  with  points  attached  to  them  be- 
come rapidly  discharged  by  the  escape  of  electricity  from 
the  point.  When  points  connected  with  the  earth  are  pre- 
sented to  charged  bodies,  the  bodies  become  rapidly  neu- 
tralized by  the  escape  of  the  opposite  electricity  from  the 
point  to  them. 

Fig.  340. 


386.  Electrical  Machine.  —  A  common  form  of  an  elec- 
trical machine  is  shown  in  Figure  340.  It  has  a  circular 
glass  plate,  which  turns  on  an  axis  supported  by  two 
wooden  uprights.  The  plate  turns  between  two  pairs  of 
cushions,  one  above  and  the  other  below  its  axis.  In  front 
of  the  plate  are  two  metallic  conductors  supported  on  glass 
legs.  An  arm  studded  with  metallic  points  directed 
towards  the  front  of  the  plate  is  connected  with  each  of 


NATURAL    PHILOSOPHY.  319 

these  conductors.  The  plate  becomes  charged  with  posi- 
tive electricity  by  friction  as  it  turns  between  the  cushions, 
and  acts  upon  the  points  by  induction.  Negative  electri- 
city escapes  from  the  points  to  the  plate,  neutralizing  the 
positive  electricity,  while  positive  electricity  accumulates 
on  the  conductors.  The  cushions  are  connected  with  the 
earth  to  allow  the  negative  electricity  developed  on  them 
to  pass  off.  To  avoid  loss  of  electricity  from  the  portion 
of  the  plate  which  is  passing  from  the  cushions  to  the 
points,  it  is  covered  with  sectors  of  oiled  silk  on  both 
sides. 

Every  electrical  machine  may  be  considered  as  a  kind 
of  electrical  pump  for  raising  electricity  to  a  higher  poten- 
tial. With  the  frictional  machine  only  a  small  quantity  of 
electricity  is  developed,  but  it  is  raised  to  an  enormously 
high  potential. 

387.  The  Electric  Wind. — The  electricity  which  escapes 
from  a  point  charges  the  molecules  of  air  in  front  of  it, 
which  are  then  repelled  by  the  point.     As  new  molecules 
come  in  to  take  the  place  of  Fig  34I< 

these,  they  are  again  charged 
and  repelled.  In  this  way  a 
current  of  air  is  made  to  set 
off  from  the  point,  which  may 
be  felt  by  the  hand  or  be 
made  to  flare  the  flame  of 
a  candle  if  the  point  is  con- 
nected with  the  conductor  of 
an  electrical  machine  (Fig- 
ure 341). 

388.  The  Electric  Mill.  —  The  electric  mill  (Figure  342) 
consists  of  a  set  of  metallic  arms  which  radiate  horizon- 
tally from  a  centre  which  is  poised  upon  a  point  so  as  to 
turn  freely.     The  arms  are  pointed  at  the  ends  and  all 
bent  around  in  the  same  direction.      When  the  mill  is 


320  NATURAL    PHILOSOPHY. 

connected  with  the  conductor  of  an  electrical  machine  in 
action,  the  arms  revolve  in  a  direction 
opposite  to  that  in  which  their  ends  point. 
The  motion  of  the  mill  is  due  to  the  re- 
action of  the  molecules  of  the  air  upon 
the  points.  The  electric  force  acts  as 
a  stress  of  repulsion  between  the  mole- 
cules and  the  points,  pushing  them  in 
opposite  directions. 

F.  ELECTRICAL  CONDENSATION. 

389.  Electrical  Capacity. — The  electrical  capacity  of  a 
conductor  is  measured  by  the  amount  of  electricity  required 
to  charge  it  to  a  unit  of  potential.     The  higher  the  poten- 
tial to  which  a  given  amount  of  electricity  will  charge  a 
conductor,  the  less  its  electrical  capacity. 

390.  The  Capacity  of  a  Conductor  increases  with  the  Ex- 
tent of  its  Surface.  —  Suspend  a  large  and  a  small  tea-can- 
ister by  silk  cords,  and  charge  equally  two  metallic  balls  of 
the  same  size  and  hung  on  silk  threads,  by  bringing  them 
both  in  contact  with  the  conductor  of  an  electrical  machine 
and  then  with  each  other.     Lower  one  of  the  balls  into 
each  of  the  canisters  so  as  to  touch  it.     Test  each  of  the 
canisters  with  an  electrometer.     The  smaller  canister  will 
be  found  to  have  the  higher  potential,  and  as  each  received 
exactly  the  same  amount  of  electricity,  it  must  have  the 
smaller  capacity. 

391.  The  Capacity  of  a  Conductor  increases  with  its  Facil- 
ities for  Induction.  —  Place  a  sheet  of  tin-foil  upon  the  top 
of  a  dry  glass  plate  provided  with  insulating  handles,  and 
connect  the  foil  to  the  gold-leaf  electroscope  by  means  of 
a  fine  wire,  which  may  be  held  to  the  foil  by  a  small  weight, 
as  shown   in   Figure  343.     The  sheet  of   foil   should  be 
somewhat  smaller  than  the  plate.    Rest  the  glass  plate  and 


NATURAL   PHILOSOPHY.  321 

foil  on  an  insulating  stand  so  as  to  separate  it  a  foot  or  so 
from  the  table.  Place  a  second  sheet  of  tin-foil  or  of  tin 
on  the  table  at  the  foot  of  the  stand.  Transfer  enough 
electricity  to  the  tin-foil  upon  the  glass  plate,  by  rubbing 
the  little  weight  on  it  carefully  with  an  excited  tube,  to 
cause  the  gold  leaves  to  diverge  strongly.  Take  the  glass 
plate  by  its  insulating  handles  and  lower  it  upon  the  tin- 
foil on  the  table.  The  gold  leaves  will  partially  collapse. 
Raise  the  glass  plate  again,  and  the  gold  leaves  will  diverge. 
Now  as  the  tin-foil  on  the  glass  plate  has  the  same  amount 
of  electricity  on  it  all  the  time,  its  capacity  must  increase 

Fig.  343- 


n 

as  it  comes  nearer  the  tin-foil  on  the  table,  since  its  poten- 
tial then  falls.  As  it  comes  nearer  the  tin-foil  on  the  table, 
its  facilities  for  induction  increase. 

The  facilities  of  a  conductor  for  induction  increase  with 
the  thinness  of  the  insulator  which  separates  it  from  neigh- 
boring conductors,  and  with  the  specific  inductive  capacity 
of  the  insulator. 

392.  Electrical  Condensation.  —  The  lowering  of  the  po- 
tential of   a  charge    by  increasing  the  conductor's  facili- 
ties  for   induction    is    called   electrical  condensation.     The 
greater  the  condensing  power,  the  greater  the  capacity  of  a 
conductor.     An  instrument  for  increasing  the  capacity  of 
a  conductor  by  condensation   is  called  an  electrical  con- 
denser, or  accumulator. 

393.  The   Action   of  Condensers.  —  The  action  of   con- 


322 


NATURAL    PHILOSOPHY. 


densers  is  illustrated  in  Figures  344  and  345.  The  metallic 
plates  A  and  B  are  separated  by  a  thin  plate  of  glass, 
C.  B  is  connected  with  the  conductor  of  an  electrical 

Fig.  344- 


machine,  and  A  is  connected  with  the  earth.     As  positive 
electricity  passes  to  the  plate  B,  it  acts  upon  A  by  induc- 
tion, drawing  negative  electricity  next  to   the  glass,  and 
Fig.  34S.  repelling  positive  electricity 

to  the  earth.  This  negative 
electricity  tends  to  draw  the 
positive  electricity  of  B  to  the 
side  m  next  to  the  glass  and 
to  hold  it  there  ;  a  part  of 
the  electricity  of  £,  however, 
remains  on  the  side/.  As 
electricity  passes  to  B  from  the  machine  the  accumulation 
of  positive  and  negative  electricities  on  m  and  n  goes  on 
increasing,  and  also  the  amount  of  electricity  on  /.  This 
will  continue  till  the  potential  of  p  is  equal  to  that  of  the 
conductor  of  the  machine.  The  condenser  has  then  re- 
ceived its  maximum  charge  from  the  source  of  electricity. 
The  electricities  on  m  and  n  are  fixed  by  their  mutual 
attractions,  while  that  on/  is  free. 

The  capacity  of  the  condenser  increases  with  the  size  of 


NATURAL    PHILOSOPHY.  323 

its  metallic  plates  and  with  its  inductive  power.  The 
inductive  power  increases  with  the  thinness  of  the  insu- 
lating plate  C,  and  with  its  specific  inductive  capacity. 

The  insulating  plate  is  in  a  state  of  strain,  and  if  it  be 
made  too  thin,  the  stress  upon  it  is  so  great  that  it  breaks 
under  the  strain  and  the  electricities  rush  together  through 
it. 

Owing  to  the  strong  attraction  of  the  electricities  on  the 
opposite  sides  of  the  insulator  for  each  other,  a  condenser 
will  retain  its  charge  a  long  time. 

Disconnect  A  from  the  earth,  and  B  from  the  machine. 
Touch  A  with  the  finger,  and  no  electricity  will  escape  from 
it,  for  all  the  electricity  on  A  is  fixed  on  the  side  next  the 
glass.  Remove  the  finger  from  A  and  touch  B.  The  free 
electricity  on  /  escapes  from  B  and  the  ball  at  b  falls. 
The  escape  of  a  part  of  the  electricity  from  B  releases  a 
part  of  the  negative  electricity  on  n,  Fig.  346- 

which  becomes  free.  Consequently 
the  ball  a  rises.  Remove  the  finger 
from  B  and  touch  A.  Its  free  elec- 
tricity will  escape,  a  will  fall,  a  part 
of  the  positive  electricity  will  be  set 
free,  and  b  will  rise.  By  touching 
each  plate  alternately  the  condenser 
will  be  gradually  discharged.  If  a 
bent  metallic  rod  be  brought  in  con- 
tact with  both  A  and  B  at  the  same 
time  (Figure  346),  the  condenser  will 
be  suddenly  discharged  through  the  rod. 

394.  The  Leyden  Jar.  —  The  Ley  den  jar  is  an  electrical 
condenser.  In  its  common  form  it  consists  of  a  wide- 
mouthed  bottle  of  hard  white  glass  (Figure  347),  coated 
inside  and  out  with  tin-foil.  The  tin-foil  stops  a  few 
inches  from  the  mouth  of  the  bottle.  The  bottle  is 
closed  with  a  lid  of  hard  wood,  in  the  centre  of  which 


324 


NATURAL   PHILOSOPHY. 


Fig.  347- 


is  a  brass  rod  with  a  ball  at  its  top.  A  chain  hangs 
from  the  lower  end  of  the  brass  rod  and  touches  the  in- 
side tin-foil. 

The  inside  foil  can  be  charged  with 
positive  electricity  by  placing  the  ball 
near  the  positive  pole  of  an  electrical 
machine,  and  working  the  machine  as 
long  as  the  sparks  will  pass.  When 
sparks  refuse  to  pass,  the  inner  foil 
is  charged  almost  to  the  potential  of 
the  pole  of  the  machine.  This  posi- 
tive charge  acts  inductively  through  the 
glass,  and  induces  a  negative  charge 
on  the  inside  of  the  outer  tin-foil,  and 
a  positive  charge  on  its  outside.  If 
the  outer  tin-foil  is  connected  to  earth,  the  positive  elec- 
tricity is  driven  off  into  the  earth,  while  the  negative  elec- 
tricity is  held  next  to  the  glass. 

Fig.  348. 


The  jar  may  be  gradually  discharged  by  alternate  con- 
tacts, as  in  the  preceding  case,  by  an  arrangement  shown 
in  Figure  348.  The  rod  connected  with  the  inner  coating 
has  a  bell  upon  the  top  of  it,  while  a  second  bell  on  a 


NATURAL    PHILOSOPHY.  325 

metallic  rod  is  connected  with  the  outer  coating  by  means 
of  a  strip  of  tin-foil  on  the  base.  A  small  metallic  ball  is 
hung  between  the  bells  on  a  silk  thread.  The  ball  is  first 
attracted  by  the  positive  bell,  and  becomes  charged  with 
positive  electricity.  It  is  then  repelled  to  the  other  bell, 
which  has  become  negative  by  the  release  of  some  of  the 
negative  electricity  on  the  outer  tin-foil,  owing  to  the  re- 
moval of  some  of  the  positive  electricity  from  the  inner 
tin  coating  of  the  jar.  It  gives  up  its  positive  electricity 
to  this  bell,  and  is  then  again  attracted  to  the  positive 
bell. 

The  jar  may  be  suddenly  discharged  by  means  of  a  dis- 
charging rod,  as  shown  in  Figure  349.  The  outside  coating 
is  touched  with  one  end  of  the  Fig  349- 

discharging  rod,  while  the  other 
end  is  brought  near  the  ball. 
There  are  now  two  strains 
going  on ;  one  is  the  strain  of 
the  glass  which  is  constant, 
and  the  other  is  the  strain  of 
the  air  between  the  ball  and 
discharging  rod,  which  increases 
as  they  come  nearer  together. 
At  last  a  point  is  reached  when  the  air  is  no  longer  able  to 
resist  the  straining  force,  and  the  electricities  burst  through 
it  and  combine  with  a  flash  and  a  report.  Immediately 
after  this  has  occurred,  the  jar  is  found  to  be  completely 
discharged. 

After  a  short  time,  however,  the  jar  will  be  found  to 
have  acquired  again  a  small  charge.  This  second  charge 
is  called  the  residual  charge. 

"  The  phenomena  of  residual  charge  can  be  explained  only 
by  supposing  the  induction  passing  through  the  glass  to  be  a 
state  of  strain  of  the  particles  of  the  glass.  On  this  hypothesis 
we  suppose  the  glass  in  the  charged  jar  to  be  very  much  strained, 


326  NATURAL    PHILOSOPHY. 

but  not  to  be  perfectly  elastic.  On  the  tin-foils  being  discharged 
—  that  is,  on  the  removal  of  the  straining  force  —  the  particles 
of  glass  instantly  fly  back  almost,  but  not  quite,  to  their  normal 
unstrained  position.  For  a  moment  we  then  have  the  tin-foils 
discharged,  but  the  glass  in  a  slightly  strained  state.  In  the 
course  of  a  few  minutes  the  glass  slowly  recovers  from  this 
residual  strain. 

"  Thus,  while  the  inner  tin-foil  has  remained  insulated,  a 
change  has  occurred  in  the  electrical  arrangement  of  the  parti- 
cles of  glass  near  it.  The  state  of  strain  has  altered. 

"  Now  in  the  ordinary  phenomena  of  induction,  the  effect  of 
altering  the  state  of  strain  of  an  insulator  (by  bringing  a  charged 
body  near  it)  is  to  induce  a  charge  on  any  adjoining  conductor. 

"  In  the  present  case  the  residual  charge  is  produced  by  the 
change  from  a  more  to  a  less  strained  state,  which  takes  place 
in  the  glass  by  virtue  of  its  elasticity. 

"  A  further  proof  that  the  phenomena  of  the  Leyden  jar  are 
the  effects  of  strain  is  found  in  the  fact  that  any  mechanical 
agitation  of  the  particles  of  the  glass,  which  enables  them  to 
move  more  freely  over  one  another,  hastens  the  development  of 
the  residual  charge." 

395.  Large  Condensers.  —  Sometimes  a  condenser  of 
very  large  surface  is  formed  by  placing  a  great  number 
of  alternate  plates  of  insulator  and  tin-foil  together.  In 
this  case  the  ist,  3d,  5th,  etc.  tin-foils  are  connected  to- 
gether, and  correspond  to  one  coating  of  the  Leyden  jar, 
and  the  2d,  4th,  6th,  etc.  are  connected  and  correspond  to 
the  other.  The  insulator  in  these  large  condensers  is  some- 
times mica  and  sometimes  paper  which  has  been  dipped  in 
melted  paraffine  wax. 

Messrs.  Clark  and  Muirhead's  great  condenser,  which 
has  been  constructed  for  "  duplexing "  the  direct  United 
States  cable,  contains  100,000  square  feet,  or  more  than 
2  acres  of  tin-foil,  and  fills  70  boxes  each  2  feet  long,  i^ 
feet  wide,  and  7  inches  deep. 

By  means  of  these  condensers  large  charges  of  electricity 
may  be  obtained  from  sources  of  low  potential. 


NATURAL    PHILOSOPHY.  327 

G.    ELECTRICAL  DISCHARGE. 

396.  Holies  Electrical  Machine,  —  Holtz's  electrical  ma- 
chine is  one  of  the  most  powerful  machines  ever  yet  in- 
vented for  obtaining  electricity  of  high  potential.  In  its 
simplest  form  it  consists  of  two  rather  thin  discs  of  glass 
placed  near  together  in  a  vertical  position,  as  shown  in 
Figure  350.  One  of  these  discs  is  capable  of  turning 
rapidly  on  a  horizontal  axis  which  passes  through  a  hole 
in  the  centre  of  the  other  disc,  which  is  stationary.  The 

Fig-  35°- 


rotating  disc  is  a  little  smaller  than  the  other  and  has  no 
openings  in  it.  There  are  .two  apertures,  called  windows, 
in  the  stationary  disc  at  the  ends  of  a  horizontal  diameter. 
Just  above  one  of  these  windows  and  below  the  other, 
there  is  a  paper  sector  fixed  upon  the  disc.  Blunt  tongues 
of  paper  run  from  each  sector  through  the  window  so  as  to 
touch  lightly  the  rotating  disc.  We  will  call  the  stationary- 
disc  the  back  of  the  machine  and  the  rotating  disc  the 
front.  In  front  of  the  rotating  disc  there  is  a  metallic 
comb  with  its  points  towards  the  disc  and  just  in  front  of 
the  tongues  from  the  paper  sectors.  These  combs  are 
connected  with  the  discharging  rods,  which  constitute  the 
poles  of  the  machine.  Under  each  discharging  rod  is  a 
small  condenser. 


328  NATURAL   PHILOSOPHY. 

On  beginning  to  use  the  machine,  it  is  necessary  to 
charge  the  two  paper  sectors,  one  with  positive  and  the 
other  with  negative  electricity. 

"  One  of  the  sectors  is  usually  charged  with  negative  elec- 
tricity  by  induction   or   friction.       The   discharging   rods   are 
p.        t  brought  in  contact,  as  shown  in 

Figure  351.  Suppose  the  sec- 
tor A  (placed  a  little  one  side 
for  convenience  of  representa- 
tion) charged  with  negative 

II.  -i  ^-  . £tiri:     electricity.     It  will    act  induc- 

\  \\    ^^^  il  *       tively  through  the  rotating  disc 

^-^^  •/ I'  upon  the  points   A',  and   draw 

positive  electricity  out  of  them 
upon  the  glass,  and  drive  neg- 
ative electricity  to  the  points  B'. 
This  electricity  will  act  inductively  upon  the  sector  B  b,  charg- 
ing its  base  B  with  positive  electricity  and  its  point  £with  nega- 
tive'electricity.  The  negative  electricity  will  escape  from  the 
points  B'  and  b  to  the  front  and  rear  surfaces  of  the  rotating 
disc.  The  disc  is  turned  in  the  direction  of  the  arrows,  or 
against  the  tongues  from  the  sectors.  As  the  disc  passes  b  and 
B'  in  its  first  revolution,  both  its  front  and  rear  surfaces  will 
become  charged  with  negative  electricity.  As  these  negative 
electricities  come  round  to  a,  they  act  inductively  upon  the 
sector  A  a,  and  upon  the  points  A'.  They  charge  the  point  a 
of  the  sector  with  positive  electricity,  and  increase  the  negative 
charge  on  the  base  A.  The  sector  j5,  the  sector  A  with  its 
increased  charge  and  both  surfaces  of  the  disc  now  act  induc- 
tively upon  the  points  A'  so  as  to  tend  to  cause  positive  elec- 
tricity to  escape  from  them.  Hence  more  than  enough  electricity 
to  neutralize  the  front  surface  of  the  rotating  disc  will  escape 
from  these  points  to  the  disc.  Also  both  surfaces  of  the  rotat- 
ing disc  as  they  come  to  #,  and  the  positive  electricity  which 
escapes  from  A'  will  act  inductively  upon  a  so  as  to  cause  posi- 
tive electricity  to  escape  from  it.  Hence  more  than  enough 
electricity  will  escape  from  it  to  neutralize  the  negative  electricity 
on  the  rear  surface  of  the  rotating  disc.  Hence,  as  the  disc 


NATURAL    PHILOSOPHY.  329 

passes  the  point  A'  and  a,  both  its  front  and  rear  surfaces  be- 
come charged  with  positive  electricity.  As  these  positive  elec- 
tricities come  round  to  6,  they  act  inductively  upon  the  sector 
B  b  and  the  points  B'  in  such  a  way  as  to  increase  the  positive 
charge  at  B,  and  as  to  cause  more  than  enough  negative  elec- 
tricity to  escape  from  the  points  b  and  B'  to  neutralize  the  posi- 
tive electricities  on  the  surfaces  of  the  disc.  Hence,  as  the  disc 
passes  the  points  b  and  Z?',both  its  surfaces  become  again  charged 
with  negative  electricity.  Thus,  both  the  surfaces  of  the  disc 
above  will  be  all  the  time  charged  with  negative,  and  below  with 
positive  electricity.  As  the  disc  is  rotated,  the  charge  on  the 
sectors  A  and  B  increases  till  it  reaches  a  maximum  which  can- 
not be  passed. 

397.  Spark  Discharge.  —  On  separating  the  discharging 
rods  of  a  Holtz  machine,  and  rotating  the  disc  rapidly,  a 
torrent  of  sparks  will  pass  between  the  rods.  These  sparks 
are  due  to  the  passage  of  electricity  through  the  air  be- 
tween them.  The  spark  is  the  ordinary  form  of  electrical 
discharge  through  dry  gases  of  the  ordinary  density. 

The  spark  is  of  very  short  duration.  It  lasts  less  than 
one  thousandth  of  a  second.  The  spark  is  very  brilliant, 
and  the  impression  of  its  light  lasts  much  longer  than  the 
spark  itself.  The  short  duration  Fig.  352. 

of  the  spark  may  be  shown  by 
the  following  experiment.  A  disc 
(Figure  352)  divided  into  a  number 
of  sectors  alternately  black  and 
white  is  put  into  rapid  rotation.- 
The  colors  of  the  sectors  blend  in 
the  eye  so  that  the  sectors  become 
utterly  undistinguishable,  and  the 

disc  appears  of  a  uniform  gray.  If  the  rotating  disc  is 
placed  in  a  darkened  room  so  as  to  be  illuminated  by  a 
succession  of  electric  sparks,  each  sector  becomes  perfectly 
distinct,  and  the  disc  appears  to  be  standing  still.  The 
disc  is  visible  only  while  the  light  of  the  spark  is  upon  it, 


330 


NATURAL    PHILOSOPHY. 


and  the  duration  of  the  light  is  so  short  that  the  disc  does 
not  have  time  to  turn  an  appreciable  amount  while  the 
light  is  on  it. 

The  light  of  the  spark  is  due  to  the  fact  that  the  line  of 
air  through  which  the  electricity  passes  is  heated  white-hot 
by  the  electric  discharge.  The  sound  of  the  spark  is  due 
to  the  sudden  expansion  and  contraction  of  this  heated 
line  of  air. 

Fig.  353- 


When  the  spark  is  short  it  is  usually  straight.  When  it 
is  long,  the  spark  becomes  zigzag  and  branching,  as  shown 
Fig.  354.  in  Figure  353. 

398.  The  Spangled  Pane.  —  If 
a  number  of  pieces  of  tin-foil 
are  arranged  on  a  plate  of  glass 
a  little  way  apart,  and  an  electric 
discharge  is  allowed  to  pass 
through  them,  sparks  will  be  ob- 
tained at  every  interval  between 
the  pieces  of  foil  where  the  elec- 
tricity is  obliged  to  pass  through 
the  air. 

Very  pretty  effects  may  be  ob- 
tained by  pasting  a  long  strip  of 
tin-foil  on  a  pane  of  glass  in 
parallel  lines  connected  at  alter- 


NATURAL    PHILOSOPHY.  331 

nate  ends,  between  a  knob  at  the  top  and  at  the  bottom 
of  the  pane  (Figure  354),  and  then  tracing  a  design  on  the 
pane  by  means  of  a  sharp  point,  which  cuts  through  the 
strips  of  tin-foil  wherever  the  lines  of  the  pattern  cross 
them.  If  a  discharge  is  allowed  to  pass  between  the  knobs, 
the  design  comes  out  in  light,  a  spark  being  produced 
wherever  a  strip  of  tin-foil  is  cut  through.  Such  a  pane 
of  glass  is  called  a  spangled  pane.  When  the  two  knobs 
of  the  pane  are  connected  to  the  two  discharging  rods  of  a 
Holtz  machine  in  action,  the  effect  is  very  pleasing.  The 
rod  or  wire  from  one  of  the  knobs  should  not  quite  touch 
the  discharging  rod  of  the  machine.  An  interval  of  half 
an  inch  should  be  left  for  sparks  to  pass. 

399.  Auroral  Discharge.  —  An  auroral  tube  is  a  long 
tube  of  glass,  of  an  inch  and  a  half  or  two  inches  internal 
diameter,  closed  at  the  ends  with  brass  caps  through  which 
pass  metallic  rods  terminating  within  the  tube  and  near  its 
ends  in  small  brass  balls  or  points.  One  of  the  caps  is 
fitted  with  a  stop-cock  for  exhaustion  of  the  air  from  the 
interior.  If  this  tube  is  screwed  to  the  plate  of  an  air- 
pump,  and  the  caps  are  connected  with  the  discharging 
rods  of  a  Holtz  machine,  it  will  be  found,  on  putting  the 
machine  in  action  and  working  the  air-pump  at  the  same 
time,  that  a  longer  spark  can  be  obtained  in  a  partial 
vacuum  than  in  air  of  the  ordinary  density.  It  will  also 
be  found  that  the  appearance  of  the  discharge  changes  as 
the  exhaustion  proceeds.  The  light  becomes  softer  and 
more  diffused  until  finally  the  whole  tube  is  filled  with  a 
pale  light.  At  the  same  time  the  noise  of  the  spark  is 
diminished  till  the  discharge  becomes  inaudible. 

This  form  of  discharge,  which  is  common  to  all  highly 
rarefied  gases,  is  called  the  auroral  discharge,  or  the 
vacuum  discharge.  The  color  of  the  light  in  this  discharge 
changes  with  the  gas  used. 

Tubes  containing  various  gases  in  a  highly  rarefied  state 


332  NATURAL   PHILOSOPHY. 

are  often  prepared  and  sealed  up  so  as  to  be  ready  for  use 
without  the  trouble  of  exhaustion.  These  tubes  are  called 
Geissler's  tubes,  or  vacuum  tubes. 

The  light  of  the  auroral  discharge  has  great  power  of 
exciting  fluorescence.  Hence,  if  any  portion  of  the  glass 
of  the  tube  is  colored  with  a  fluorescent  substance,  as  ura- 
nium, or  any  portion  of  the  tube  passes  through  a  fluores- 
cent liquid,  as  a  solution  of  sulphate  of  quinine,  when  the 
discharge  takes  place,  the  uranium  glass  glows  with  a  soft 
green  light,  and  the  sulphate  of  quinine  with  a  soft  blue, 
each  becoming  fluorescent.  The  accompanying  plate  rep- 
resents a  vacuum  tube.  The  spiral  portion  near  each  end 
passes  through  a  solution  of  sulphate  of  quinine  contained 
in  a  wider  external  tube.  The  green  portions  are  colored 
with  uranium. 

The  red  shows  the  natural  color  of  the  discharge  in 
rarefied  air.  The  sulphate  of  quinine  is  quite  colorless  by 
ordinary  daylight,  and  the  uranium  very  nearly  so. 

400.  The  Glow  Discharge.  —  When  a  metallic  point  is 
attached  to  the  conductor  of  an  electrical  machine  in  ac- 
tion, it  will  be  seen  in  the  dark  to  be  covered  with  a  soft 
glow  of  light.     We  have  seen  that  in  this  case  a  stream  of 
molecules  of  air  sets  off  from   the  point,  and  that  these 
molecules  carry  electricity  away  with  them,  and   so  dis- 
charge the  conductor.     This  discharge  is  called  connective 
discharge.      The  surfaces   between  which    convective   dis- 
charge is  taking  place  are  covered  with   a  faint  glow  of 
light.      Hence  convective  discharge  is  often  called  glow 
discharge.      In  spark  discharge  the  electricity  leaps  from 
molecule  to  molecule  through  the  intervening  air,  while  in 
convective  discharge  the  electricity  is  carried  along  by  the 
molecules  which  traverse  the  intervening  space. 

401.  Brush  Discharge.  —  Remove  the   condenser  from 
under  the  discharging  rods  of  a  Holtz   machine,  put  the 
machine  in  action,  and  separate  the  rods.     Instead  of  the 


NATURAL    PHILOSOPHY.  333 

ordinary  spark  discharge  we  shall  find  the  space  between 
the  rods  filled  with  a  pale,  diffused  purplish  light.  From 
the  form  of  this  light,  this  discharge  has  been  called  the 
brush  discharge. 

The  brush  discharge  seems  to  be  a  blending  of  the  spark 
and  the  convective  discharge.  The  electricity  is  some  of 
the  time  carried  by  the  molecules  of  the  air,  and  some 

Fig.  355- 


of  the  time  it  leaps  along  from  molecule  to  molecule.  In 
a  darkened  room  brushes  of  light  will  be  seen  on  various 
parts  of  a  powerful  Holtz  machine  in  action.  The  brush 
sometimes  assumes  the  form  shown  in  Figure  355. 


334  NATURAL  PHILOSOPHY. 

II. 

VOLTAIC   ELECTRICITY. 
A.    DEFLECTION  OF  THE  NEEDLE.  - 

402.  The  Electric   Current.  —  The    flow   of    electricity 
through   a  conductor  is  called  the  electric  current.      The 
phenomena  of   electricity  in  motion,  or  of   current  elec- 
tricity,   are  usually  classed  together  under  the   head   of 
voltaic  electricity,  to  distinguish  them  from  those  of  electri- 
city at  rest,  or  of  frictional  electricity.     The  former  depart- 
ment of  electricity  is  sometimes  called  dynamical  electricity, 
electro-dynamics,  or  electro-kinetics;   and  the  latter,  statical 
electricity,  or  electro-statics.    The  term  electro-kinetics,  which 
is  the  more  modern  term,  is  from  two  Greek  words  meaning 
electricity  and  motion. 

403.  Action   of  Current  on  Magnetic  Needle.  —  Oersted 
discovered,  in  1819,  that  a  current  flowing  through  a  wire 
near  a  magnetic  needle,  which  is  poised  so  as  to  turn  freely 
in  any  direction,  would  deflect  the  needle.     If  the  wire  is 
held  over  the  needle  (Figure  356),  the  needle  will  be  de- 

Fig  3j6  fleeted  in  one  direction.     If  the  same 

wire  is  held  under  the  needle  (Figure 

*^f?  357)>  tne  needle  will  be  deflected  in 

Fig.  357.  the  opposite   direction.      If   the   cur- 

rent is  made  to  flow  in  the  opposite 
direction  through  the  wire  while  over 


or  under  the  needle,  the  needle  will  be  deflected  in  the 
opposite  direction  to  what  it  was  before. 

If  two  currents  flow,  one  over  the  needle  in  one  direc- 
tion, and  one  under  the  needle  in  the  opposite  direction, 
they  will  both  tend  to  turn  the  needle  the  same  way.  In 
any  case,  the  stronger  the  current  the  greater  the  deflec- 
tion of  the  needle. 

If  the  wire  conveying  it  is  bent  round  the  needle,  as 


NATURAL    PHILOSOPHY. 


335 


in  Figure  358,  the  current  will  flow  in  opposite  directions 
above  and  below  the  needle.  Hence  both  portions  of  the 
current  will  tend  to  turn  the  needle  the  same  way,  and  the 
deflection  will  be  greater  than  when  the  current  flowed  sim- 
ply over  or  under  the  needle.  If  the  wire  is  carried  a  sec- 
Fig-  35*-  Fig.  359- 


C 


ond  time  around  the  needle  (Figure  359),  the  deflection  of 
the  needle  will  be  increased,  since  there  will  now  be  two 
currents  above  the  needle  and  two  below  it,  all  tending  to 
turn  the  needle  the  same  way. 

404.   Ampere's  Rule.  —  Ampere  has  given  the  following 
Yule  for  ascertaining  the  direction  of  the  deflection  of  the 

Fig.  360. 


needle  in  any  case  :  Imagine  a  little  swimmer  in  the  elec- 
tric current,  always  swimming  with  the  current,  and  with 
his  face  to  the  needle.  The  north  pole  of  the  needle  will 
always  be  deflected  to  his  left  (Figure  360). 

405.  Simple  Galvanometer.  —  A  galvanometer  is  an  instru- 
ment for  showing  the  presence,  direction,  and  strength 
of  an  electrical  current.  A  simple  galvanometer  consists 


1 


336  NATURAL    PHILOSOPHY. 

of  a  magnetic  needle,  free  to  turn  in  a  horizontal  or  verti- 
cal plane,  and  surrounded  with  a  coil  of  wire.  -This  gal- 
vanometer shows  the  presence  of  a  current  in  the  wire  with 
which  it  is  connected,  by  the  deflection  of  the  needle ;  the 
direction  of  the  current,  by  the  direction  in  which  the  nee- 
dle is  deflected ;  and  the  strength  of  the  current,  by  the 
amount  of  the  deflection. 

406.  Astatic  Needle.  —  The  directive  action  of  the  earth 
upon  a  magnetic  needle  impedes  its  deflection  by  the  cur- 
Fig.  36i.  rent.      This    directive    action  may  be 

neutralized  by  combining  two  needles, 
as  shown  in  Figure  361.     The  needles 
are   fastened  together    rigidly    at   the 
T  centre  ;  and   the   poles  of  one   needle 

s  are  the  reverse  of  those  of  the  other. 
As  there  is  a  north  and  a  south  pole  at  each  end  of  the 
combination,  each  needle  must  neutralize  the  directive 
action  of  the  earth  upon  the  other.  Such  a  combination 
of  needles  is  called  an  astatic  needle  (unsteady  needle). 

407.  Astatic  Galvanometer.  —  An  astatic  galvanometer  is 
one  in  which  an  astatic  needle  is  used.     The  two  needles 

Fl5-  362.  of  tiie  combination  are  almost, 

but  not  quite,  of  the  same 
strength.  The  needles  are 
hung  on  a  fibre  of  silk,  and 
the  wire  is  coiled  around  the 
lower  needle  (Figure  362). 
It  will  be  seen  by  Ampere's 
rule  that  the  current  that  flows 

between  the  needles  will  tend  to 

turn  both  needles  the  same  way, 

while  that  which  flows  under  the  lower  needle  will  tend  to 
turn  the  needles  in  opposite  directions.  Owing  to  the 
greater  distance,  its  action  on  the  upper  needle  will  be 
much  feebler  than  its  action  on  the  lower  needle.  Such  a 


NATURAL    PHILOSOPHY. 


337 


galvanometer  is  very  sensitive,  since  the  directive  action  of 
the  earth  is  nearly  neutralized,  while  the  effective  action 
of  the  current  is  increased  by  the  use  of  two  needles. 

When  it  is  desired  to  make  this  galvanometer  extremely 
sensitive,  the  needles  are  made  very  light,  and  are  hung  on 

Fig-  363-  Fig.  364. 


c 

a  single  fibre  of  silk,  and 
the  wire  is  coiled  several 
thousand  times  around  the 
lower  needle.  In  this  case 
the  wire  is  very  fine,  and  is 
wound  on  a  flat  reel,  of  the 
form  shown  in  Figure  363. 
The  whole  is  enclosed  in  a 
glass  case,  to  protect  the 
needle  from  currents  of  air  (Figure  364). 

408.     Thomson's   Reflecting    Galvanometer. — The    most 
sensitive  galvanometers  ever  constructed  are  Thomson's 
reflecting  galvanometers.    These  galvanome-        Fig  ^ 
ters    are  sometimes  astatic   and  sometimes 
not.     In  the  non-astatic  form,  one  or  more 
magnets,  about  ^  of  an  inch  in  length,  are 
cemented    to  the   back   of    a   light   mirror, 
about  }£  of    an    inch    in    diameter    (Figure 
365).      The  magnets    and    mirror   together 
weigh  less  than  a  grain.     They  are  hung  on 
a  single  fibre  of  unspun  silk  in  the  centre 
of    a  circular  coil,  which   is  enclosed   in  a 
brass  cylinder.     The  front  of  this  cylinder  is  of  glass. 

To  avoid  the  inconvenience  of  always  being  obliged  to 
place  the  instrument  in    the  magnetic  meridian,  a  large 


338 


NATURAL    PHILOSOPHY. 
Fig.  366. 


NATURAL  PHILOSOPHY.  339 

curved  bar,  feebly  magnetized,  is  fixed  horizontally  on  a 
stem  above  the  case.  It  turns  with  friction  on  this  stem, 
so  that  it  may  be  placed  in  any  direction.  This  magnet,  by 
its  directive  action,  forms  "an  artificial  magnetic  meridian 
in  any  desired  direction.  A  scale  is  placed  about  a  yard  in 
front  of  the  mirror,  upon  which  a  beam  of  light  is  reflected 
from  the  mirror  (Figure  366).  The  movement  of  the  spot 
of  light  on  the  scale  magnifies  the  movement  of  the  needle. 
The  astatic  form  of  this  galvanometer  is  shown  in  Fig- 
ure 367.  Each  needle  is  surrounded  by  its  own  coil  of 
wire.  The  current  flows  through  these  coils  in  opposite 
directions. 

409.  Differential    Galvanometer.  —  A   differential  galva- 
nometer is  one  which  has  two  coils  around  the  needle,  ex- 
actly alike  in  every  respect,  except  that  they  are  wound  in 
opposite  directions.     The  deflection  of  the  needle  shows 
the  difference  in  strength  of  the  two  currents,  and  which 
is  the  stronger.      When  the  two  currents  are  equal,  the 
needle  is  not  deflected. 

B.   FLOW  OF  ELECTRICITY  THROUGH  CONDUCTORS. 

410.  Electromotive  Force. — The  flow  of  electricity  through 
a  wire  connecting  two  conductors  is  analogous  to  the  flow 
of  water  through  a  pipe  connecting  two  reservoirs.     When 
the  water  is  at  the  same  level  in  both  reservoirs,  no  water 
will  flow  through  the  pipe.     When  the  water  is  at  different 
levels  in  the  two  reservoirs,  the  water  will  flow  through  the 
pipe  from  the  higher  level  to  the  lower.     The  greater  the 
difference  between  the  levels  of  the  water  in  the  two  reser- 
voirs, the  greater  the  energy  of  the  current  in  the  pipe.    To 
keep  a  uniform  current  in  the  pipe,  the  same  difference  of 
level  must  be  maintained  between  the  two  reservoirs. 

In  like  manner,  no  current  of  electricity  will  flow  through 
a  wire  connecting  two  conductors,  when  the  conductors  are 
at  the  same  potential.  When  the  conductors  differ  in 


34° 


NATURAL  PHILOSOPHY. 


potential,  a  current  will  flow  through  the  wire  from  the 
higher  potential  to  the  lower.  The  greater  the  difference 
of  potential  between  the  two  conductors,  the  greater  the 
energy  of  the  current.  To  keep  a  uniform  current  in 
the  wire,  the  same  difference  of  potential  must  be  main- 
tained between  the  two  conductors. 

The  force  which  urges  electricity  through  a  conductor  is 
called  the  electromotive  force.  The  electromotive  force  is 
always  equal  to  the  difference  of  potential  between  the 
points  connected  by  the  wire.  A  certain  standard  electro- 
motive force  has  been  selected  as  a  unit,  and  is  called  a 
volt.  A  conductor  designed  to  convey  a  current  is  called 
a  circuit. 

411.  Electrical  Resistance. —  Every  known  substance  offers 
some  resistance  to  the  passage  of  the  current  through  it, 
but  different  substances  differ  greatly  in  the  amount  of 
resistance  which  they  offer. 

The  resistance  of  a  wire  varies  with  its  material,  its 
length,  and  its  thickness.  The  longer  and  thinner  a  wire, 
the  greater  its  resistance.  The  metals  offer  comparatively 
little  resistance  to  the  passage  of  the  current,  and  silver 

Fig.  368. 


offers  the  least  resistance  of  all  the  metals.  Copper 
stands  next  to  silver.  The  less  the  resistance  any  sub- 
stance offers  to  the  passage  of  the  current,  the  better  con- 
ductor it  is.  A  certain  standard  of  resistance  has  been 


NATURAL    PHILOSOPHY.  341 

chosen  as  a  unit,  and  is  called  an  ohm.     It  is  about  the 
resistance  of  250  feet  of  copper  wire  ^  of  an  inch  thick. 

412.  Resistance  Coils  and  Boxes. —  Coils  of  wire  offering 
various  multiples  and  submultiples  of  an  ohm  of  resistance,  called 
resistance  coils,  are  arranged  in  boxes,  called  resistance  boxes,  in 
such  a  way  that  any  amount  of  resistance  may  be  readily  intro- 
duced into  the  circuit. 

Figure  368  shows  the  top  of  the  resistance  box.  There  are 
several  lines  of  copper  plates.  The  plates  in  each  line  are  sepa- 
rated from  each  other  by  a  slight  space,  and  the  ends  of  the  plates 
are  shaped  so  as  to  furnish  a  circular  aperture  for  inserting 
brass  plugs  between  the  plates.  Under  each  aperture  there  is  a 
resistance  coil,  and  the  number  of  ohms  of  resistance  in  it  is 
marked  beside  the  aperture  on  the  top  of  the  box.  Figure  369 

Fig.  369. 


ti 


shows  the  resistance  coils  and  the  way  they  are  connected  with 
the  plates.  It  will  be  seen  that  each  coil  connects  two  copper 
plates  in  such  a  way  that  the  current  must  pass  through  the  coil 
when  the  plug  is  removed  from  the  aperture  of  a  box.  When 
the  plug  is  inserted,  the  electricity  passes  through  the  plug 
without  passing  through  the  coil. 

When  the  resistance  box  is  placed  in  the  circuit,  any  desired 
amount  of  resistance  may  be  introduced  into  the  circuit  by  re- 
moving one  or  more  of  the  plugs ;  and  the  amount  of  resist- 
ance introduced  may  be  ascertained  by  adding  the  numbers 
beside  the  apertures  from  which  the  plugs  have  been  removed. 

413.  Quantify  of  the  Current.  —  By  the  quantity  of  the 
current  we  mean  the  amount  of  electricity  flowing  through 
the  circuit  per  second.  The  unit  of  quantity  is  the  amount 
of  electricity  that  a  volt  of  electromotive  force  will  cause 
to  flow  through  an  ohm  of  resistance  in  a  second  of  time. 
It  is  called  a  weber. 

The  power  of  a  current  to  deflect  a  needle  is  directly 


342  NATURAL    PHILOSOPHY. 

proportional  to  its  quantity.  Hence  the  quantity,  or  vol- 
ume, of  the  current  is  estimated  by  its  power  of  deflecting 
a  needle. 

414.  Division  of  the  Current.  —  When  the  circuit  divides 
into  two  or  more  branches,  the  current  will  also  divide 
among  the  branches  in  such  a  way  that  the  quantity  of  the 
current  in  each  branch  will  be  inversely  proportional  to 
the  resistance  of  the  branch.  Suppose  the  circuit  divides 

Fig.  370. 


at  A  (Figure  370)  into  four  branches,  W,  X,  Y,  Z,  whose 
resistances  are  in  the  ratio  of  3,  5,  7,  and  9.  Then  ££f  of 
the  current  will  pass  through  W,  ^\  through  X,  £j>g  through 
Y,  and  $&  through  Z. 

415.  Division  of  the  Current  into  two  Equal  Parts.  —  In 
order  to  have  the  current  divide  into  two  equal  parts,  it  is 
necessary  that  the  circuit  should  divide  into  two  branches  of 
equal  resistance.  If  the  two  branches  are  not  of  the  same  re- 
sistance, their  resistances  may  be  made  equal  by  introducing  a 
set  of  resistance  coils  into  the  branch  which  offers  the  less 

Fig.  3?t- 


resistance.  Suppose  the  circuit  (Figure  371)  divides  at  A  into 
two  branches  C  and  D,  which  reunite  at  B,  and  suppose  D  offers 
less  resistance  than  C.  By  employing  a  resistance  box  at  e  we 
may  balance  the  resistance  of  C, 

416.  Measurement  of  the  Resistance  of  a  Wire  by  the  Equal 
Division  of  the  Current.  —  The  equal  division  of  the  current 
between  two  branches  whose  resistances  are  equal  affords  a 
ready  means  of  measuring  the  resistance  of  a  wire.  It  is  only 


NATURAL    PHILOSOPHY. 


343 


necessary  to  make  one  of  the  branches  C  (Figure  372),  a  resist- 
ance box,  and  the  other  branch  D  the  wire  to  be  tested,  and  to 
connect  each  branch  with  one  of  the  coils  of  the  differential 
galvanometer  G.  The  resistance  box  must  be  adjusted  until  the 
needle  of  the  galvanometer  is  not  deflected.  The  currents  in 

Fig.  372- 


the  two  branches  are  now  equal,  and  also  the  resistance  of  the 
two  branches.  The  resistance  of  the  branch  C  may  be  read  off 
from  the  resistance  box,  and  this  is  equal  to  that  of  the  wire  D. 
417.  The  Potential  of  a  Wire  through  which  a  Uniform 
Current  is  flowing.  —  Suppose  the  wire  A  E  (Figure  373),  to 
be  of  uniform  resistance  throughout,  and  that  a  uniform  cur- 
rent is  flowing  through  it  from  A  to  E.  Its  potential  will  fall 
at  a  uniform  rate  from  A  to  E.  Suppose  the  potential  at  E  to 
be  o  and  at  A  to  be  80.  Let  the  perpendicular  A  P  represent 

Fig.  373. 


A.BCDFGHK 


the  potential  at  A.  PE  will  represent  the  fall  in  potential 
from  A  to  E.  The  potential  of  any  point  along  the  wire  A  E 
will  be  represented  by  a  perpendicular  erected  at  that  point  and 
terminating  in  the  line  P  E.  Suppose  the  points  B,  C,  D,  f,  G, 
H,  and  AT,  to  be  respectively  |,  f ,  f ,  £,  f ,  f ,  and  £  of  the  way  from 
A  to  E.  Their  potential  will  be  represented  by  the  lines  B L, 
CM,  DN,FO,GQ,HR,  and  K S,  and  will  be  70,  60,  50,  40, 
30,  20,  and  10. 

In  the  above  cases,  the  wire  being  alike   throughout,   the 
resistance  increases  with  the  distance  along  the  wire.     It  fol- 


344 


NATURAL    PHILOSOPHY. 


lows,  therefore,  that  the  potential  falls  in  passing  along  the  wire 
as  the  resistance  increases.  This  is  true  of  any  wire  whatever, 
whether  of  uniform  resistance  or  not.  That  is,  if  any  wire  has 
ten  units  of  resistance,  and  its  potential  is  too  at  one  end  and 
o  at  the  other,  at  one  unit  of  resistance  from  the  first  end  the 
potential  will  be  90  ;  at  2  units,  80 ;  at  3  units,  70  ;  etc. 

Fig-  374- 


418.  Current  in  a  Wire  connecting  Two  Circuits. —  Let 
A  £  (Figure  374)  represent  a  wire  of  uniform  resistance 
throughout,  through  which  a  uniform  current  is  flowing  from 
A  to  .£",  whose  potential  at  P2  is  o,  and  at  A  50.  Let  A  P 
represent  the  potential  at  A  and  P  E  the  fall  in  potential  from 
A  to  E.  Let  B  be  a  point  %  of  the  way  from  A  to  E.  BD 
will  represent  its  potential,  which  will  be  40. 

Let  A'E'  be  a  second  wire  of  uniform  resistance  throughout, 
through  which  also  a  uniform  current  is  flowing  from  A'  to  E'. 
Suppose  the  potential  the  same  at  A'  as  at  A,  and  at  E'  as  at  £", 
and  suppose  B'  l/s  of  the  way  from  A'  to  E'.  The  potential  of 
B'  will  be  40. 

Suppose  B  and  B'  joined  by  a  wire.  No  current  will  flow 
through  this  connecting  wire,  because  B  and  B'  are  at  the  same 
potential.  Connect  B  with  any  point  between  A'  and  B' ,  and 
a  current  will  flow  through  the  connecting  wire  towards  B. 
Connect  B  with  any  point  between  B'  and  E',  and  a  current  will 
flow  through  the  connecting  wire  from  B. 


NATURAL    PHILOSOPHY.  345 

Let  iv  represent  the  resistance  of  A  B;  x  of  BE;  y  of 
A'B';  and  *  of  £'£'. 

By  construction,     A  B  :  B  E  =  A'  B'  :  B1  E1 

.-.  TV  :  x  =y  :  z. 

In  general,  when  two  wires  whose  potentials  are  the  same  at 
both  ends  are  connected  by  a  third  wire,  no  current  will  cross 
this  wire,  provided  the  resistance  of  the  first  part  of  the  first 
wire  is  to  the  resistance  of  its  second  part,  as  the  resistance  of 
the  first  part  of  the  second  wire  is  to  the  resistance  of  its  second 
part.  In  every  other  case  a  current  will  cross  the  connecting 
wire. 

419.  Wheatstone's  Bridge,  —  The  arrangement  of  the  circuit 
in    Figure    375    is    called  Fig.  37S. 
Wheatstone's  Bridge.    The 

circuit  divides  at  A  into 
two  branches,  which  re- 
unite at  E.  The  points  B 
and  B'  are  connected  by 
a  wire  called  the  bridge. 
Let  iu  =  the  resistance  of  A  B  ;  x  =  that  of  B  E  ;  y  =  that  of 
A  B';  and  z  =  that  of  B'  E.  Since  the  potentials  of  both 
branches  are  the  same  at  A  and  also  at  E,  no  current  will  cross 
the  bridge,  when  w  :  x=y  :  z.  In  every  other  case  a  current 
will  cross  the  bridge. 

420.  Measurement  of  Resistance  by  Wheatstone's  Bridge.  — 
Wheatstone's  bridge  furnishes  a  ready  means  of  measuring  the 
resistance  of  any  wire.     When  used  for  this  purpose  the  bridge 
is  arranged  as  shown  in  Figure 

376.  Three  of  the  branches, 
a/,_y,  and  z,  are  made  to  con- 
sist of  resistance  boxes,  and 
the  fourth,  JT,  of  the  wire  whose 
resistance  is  to  be  measured, 
and  a  galvanometer  is  intro- 
duced into  the  bridge.  The 
resistance  boxes  are  then  ad- 
justed until  the  needle  of  the  galvanometer  suffers  no  deflection. 
As  no  current  is  then  crossing  the  bridge,  we  shall  have 


346  NATURAL    PHILOSOPHY. 

iv  :  x  =y  :  z.  The  three  resistances,  w,  _y,  and  z,  are  obtained 
from  the  resistance  boxes,  and  x  is  .found  by  solving  the  pro- 
portion. 

421.  The  Velocity  of  the  Current.  —  A  part  of  the  electricity 
which  flows  into  a  wire  is  used  in  charging  the  wire  statically. 
The  amount  of  electricity  required  for  this  depends  upon  the 
capacity  of  the  wire,  and  this  depends  upon  its  facilities  for  in- 
duction, and  this,  in  turn,  upon  the  nearness  of  neighboring 
conductors  and  the  insulating  medium  which  separates  it  from 
them.  A  wire  strung  on  poles  some  distance  above  the  earth 
has  very  small  electrical  capacity.  One  nearer  the  earth  has 
greater  capacity,  and  a  submarine  cable  has  a  much  greater 
capacity  still.  In  the  case  of  the  cable,  induction  is  readily 
carried  on  by  the  wire  through  its  insulating  sheath  with  the 
water  outside.  The  greater  the  specific  inductive  capacity  of 
the  insulating  sheath,  the  greater  the  electrical  capacity  of  the 
cable. 

The  velocity  of  the  current  in  a  wire  depends  upon  the  resist- 
ance of  the  wire  and  upon  its  electrical  capacity.  The  greater 
either  of  these,  the  less  the  velocity  of  the  current.  Hence  the 
velocity  of  the  current  varies  greatly  under  different  circum- 
stances. It  ranges  from  about  13,000  miles  a  second  to  about 
60,000  miles  a  second ;  or  from  a  velocity  which  would  take  it 
around  the  earth  in  two  seconds  to  one  which  would  take  it 
twice  around  the  earth  in  a  second. 


C.   ELECTRO-CHEMICAL  ACTION. 

/.    VOLTAIC  BATTERIES. 

422.  Voltaic  Cell.  —  If  two  metal  plates  Z  and  C  (Figure 
377)  are  partly  immersed  in  a  liquid  which  acts  chemically 
more  powerfully  upon  one  of  them  than  upon  the  other, 
and  are  placed  in  metallic  communication  outside  of  the 
liquid,  either  by  direct  contact  or  by  means  of  a  wire,  a 
current  of  electricity  will  flow  outside  of  the  liquid  from 
the  metal  least  acted  upon  by  the  liquid  when  alone  to  the 
one  most  acted  upon. 


NATURAL    PHILOSOPHY.  347 

When  two  metals  are  arranged  as  above  described  in  a 
liquid,  and  are  in  metallic  communication,  the  one  which, 
if  alone,  would  be  least  acted 
on,  is  entirely  protected  by  the 
other.  The  arrangement  is 
called  a  voltaic  cell.  The  por- 
tion of  the  plate  least  acted  on, 
which  is  out  of  the  liquid,  is 
called  the  positive  pole  of  the 
cell,  and  the  corresponding  part 
of  the  other  plate  the  negative 
pole. 

423.  Theory  of  the  Voltaic  Cell. 
—  The  voltaic  cell  is  a  machine  for  maintaining  a  constant 
difference  of  potential  at  its  two  poles.  There  are  two  theories 
of  the  action  of  the  cell.  Gordon's  statement  of  these  theories 
is  as  follows  :  — 

"  If  two  metals  be  placed,  near  together  but  not  in  contact, 
in  a  liquid  which  acts  chemically  more  upon  one  than  upon  the 
other,  the  metals  become  charged  so  that  the  one  least  acted 
on  is  of  higher  potential  than  the  one  most  acted  on.  The  dif- 
ference of  potential  produced  depends  only  on  the  nature  of  the 
metals  and  of  the  liquid,  and  not  on  the  size  or  position  of  the 
plates. 

"  As  soon  as  the  difference  of  potential  has  reached  its  con- 
stant value,  the  chemical  action  ceases. 

"  If  now  the  metals  are  connected  by  a  wire  outside  the  liquid, 
the  difference  of  potential  begins  to  diminish,  and  an  electric 
current  flows  through  the  wire.  As  soon  as  the  difference  of 
potential  becomes  less  than  the  maximum  for  the  metals  and 
liquid,  chemical  action  recommences  and  brings  it  up  to  the 
maximum,  and  thus,  if  no  disturbing  cause  interferes,  the 
current  will  continue  till  the  metal  most  acted  on  is  entirely 
dissolved. 

"This  view  of  what  takes  place  explaips  the  action  very 
well.  It  is  not  yet  certain  whether  this  is  the  true  explanation, 
or  whether  we  should  say  :  On  joining  two  metals  either  directly 


348  NATURAL   PHILOSOPHY. 

or  by  a  wire,  a  difference  of  potential  is  observed.  When  the 
metals,  still  joined,  are  partly  immersed  in  a  liquid,  which  acts 
more  upon  one  than  upon  the  other,  the  chemical  action  equal- 
izes the  potentials,  and  in  doing  so  causes  a  flow  of  electricity 
along  the  connecting  wire.  The  moment  the  equalization  of  the 
potentials  has  commenced,  the  difference  is  renewed  again  at 
the  point  or  points  of  contact  between  the  metals  ;  and  so,  if  no 
disturbing  cause  interferes,  a  continuous  flow  of  electricity  is 
kept  up,  till  the  metal  most  acted  on  is  entirely  dissolved. 

"  The  latter  view  has,  in  my  opinion,  more  evidence  to  sup- 
port it  than  the  former." 

When  the  positive  and  negative  plates  outside  the  liquid  are 
in  metallic  connection,  either  by  direct  contact  or  by  means  of  a 
wire,  the  circuit  is  said  to  be  closed;  otherwise  the  circuit  is 
said  to  be  open. 

424.  Zinc  and  Copper  Cell.  —  In  nearly  all  practical 
forms  of  the  voltaic  cell  the  negative  plate  is  zinc.  The 
positive  plate  varies  in  material. 

The  simplest  form  of  the  voltaic  cell  consists  of  a  plate 
of  copper  and  a  plate  of  zinc  partly  immersed  in  dilute 
sulphuric  acid,  which  acts  on  the  zinc,  but  not  on  the 
copper.  With  such  an  arrangement  the  current  ceases 
after  a  very  short  time.  On  examination,  the  copper  will 
be  found  to  be  coated  with  minute  bubbles  of  hydrogen. 

When  a  piece  of  zinc  alone  is  dissolved  in  dilute  sul- 
phuric acid  (H,SO4)  it  unites  with  the  SO4,  forming 
sulphate  of  zinc  (ZnSO4),  and  sets  the  hydrogen  free. 
When  the  zinc  is  dissolved  in  the  voltaic  cell,  sulphate  of 
zinc  is  formed,  but  the  hydrogen  is  liberated,  not  at  the 
surface  of  the  zinc,  but  at  that  of  the  copper 

When  the  copper  becomes  coated  with  hydrogen,  the 
cell  fails  to  piocluce  a  difference  of  potential  and  the  cur- 
rent stops.  Why  the  hydrogen  should  appear  at  the  copper, 
and  why  it  should  stop  the  current,  is  not  well  understood. 

The  zinc  of  commerce,  of  which  battery  plates  are  made, 
contains  many  particles  of  iron  and  other  metals.  If  a 


NATURAL   PHILOSOPHY. 


349 


piece  of  ordinary  zinc  is  placed  in  acid,  each  of  these 
pieces  of. iron,  together  with  the  zinc  near  it,  forms  an 
independent  small  cell,  whose  circuit  is  always  closed 
whether  the  main  circuit  is  closed  or  not.  The  currents 
produced  in  these  small  circuits  in  no  way  help  the  main 
current,  while  they  cause  the  zinc  to  be  rapidly  consumed. 

The  cost  of  chemically  pure  zinc  prohibits  its  use,  so  a 
different  plan  is  used,  which  is  found  to  be  in  every  respect 
equally  efficacious  with  the  employment  of  pure  zinc. 

It  consists  in  coating  the  zinc  with  mercury.  This  is 
done  by  first  immersing  the  zinc  for  a  few  minutes  in  dilute 
sulphuric  or  hydrochloric  acid,  so  as  to  give  it  a  chemically 
clean  surface,  and  then  pouring  mercury  upon  it.  The 
mercury  at  once  combines  with  its  surface,  and  the  whole 
of  the  zinc  appears  bright  like  silver.  Zinc  thus  "  amal- 
gamated "  is  not  attacked  by  dilute  sulphuric  acid,  unless 
it  forms  part  of  a  closed  galvanic  circuit.  The  precise 
action  of  the  mercury  is  not  known. 

425.  Sinews  Cell.  —  In  order  that  a  cell  may  give  a  uniform 
current,  it  is  necessary  to  keep  the  hydrogen  from  collecting  on 
the  positive  plate. 

In  Smee's  cell  (Figure  378)  the  positive  plate  is  platinized 

Fig.  378.  Fig.  379. 


3$0  NATURAL    PHILOSOPHY. 

silver,  that  is,  silver  with  a  rough  deposit  of  platinum  on  its 
surface,  and  the  negative  plate  is  zinc.  The  platinum  presents 
a  multitude  of  points,  from  which  the  hydrogen  disengages  itself 
more  readily  than  from  a  smooth  surface.  As  the  silver  is  more 
expensive  than  zinc,  the  silver  plate  is  usually  placed  between 
two  zinc  ones,  so  that  both  sides  of  it  can  be  utilized. 

426.  Bichromate  of  Potash  Cell.  —  In  this  cell,  the  plates  are 
of  carbon  and  zinc,  and  the  liquid  is  dilute  sulphuric  acid  satu- 
rated with  bichromate  of  potash.     The  bichromate  absorbs  the 
hydrogen  and  thus  prevents  its  accumulation  on  the  carbon. 
One  form  of  this  cell  is  shown  in  Figure  379.     It  is  so  con- 
structed that  the  zinc  plate  can  be  drawn  out  of  the  liquid  when 
the  cell  is  not  in  use.     The  power  of  the  cell  decreases  rapidly 
when  in  action. 

427.  Two-Fluid  Cells.  —  In   all   single- fluid    cells    the 
compounds  formed  by  the  hydrogen  in  the  liquid  which 
absorbs  it  return  to  the  zinc  plate  and  retard  the  action  on 
it.   Cells  with  two  fluids  are  designed  to  prevent  this.    The 
two  principal  types  are  Grove's  and  Daniel? s  cells.     The 
latter  is  used  when  a  constant  current  of  moderate  strength 
is  required  for  days,  weeks,  or  months ;  the  former,  when 
a  very  powerful  current  is  required  for  a  few  hours. 

428.  Grove's  Cell.  —  In  Grove's  cell  the  metals  used  are 
zinc  and  platinum  ;  and  the  fluids,  strong  nitric  and  dilute 

Fig.  380.  sulphuric  acids.     A  cell  of  thin  porous 

earthenware  is  filled  with  nitric  acid, 
and  contains  the  platinum  plate.  This 
cell  (Figure  380)  is  placed  within 
another  cell  of  glass  or  vulcanite,  con- 
taining the  zinc  and  dilute  sulphuric 
acid.  The  porous  earthenware,  when 
wet,  permits  the  electricity  to  pass 
freely  through  it,  while  it  almost  en- 
tirely prevents  the  mixing  of  the  liquids.  The  nitric  acid 
absorbs  the  hydrogen  as  fast  as  it  is  set  free. 

429.  Buns  erf  s_Cell. —  Bunsen's  cell  (Figure  381)  is  simi- 


NATURAL    PHILOSOPHY. 


351 


lar  in  construction  to  Grove's,  with  the  exception  that  the 
positive   plate    is    carbon     instead    of  Fig.  381. 

platinum.  Owing  to  the  impossibility 
of  cutting  the  coke  carbon  into  thin 
slices,  the  Bunsen  cell  is  made  larger 
than  Grove's,  but  it  is  not  so  powerful, 
and  is  more  troublesome  and  expensive 
to  work. 

Both  Grove's  and  Bunsen's  cells  give 
off  fumes  of  nitrous  acid,  which  are 
unwholesome,  and  injurious  to  instru- 
ments. This  inconvenience  may  be 
obviated  by  using  a  solution  of  bichro- 
mate of  potash  in  the  porous  cup  in- 
stead of  nitric  acid.  This  arrangement  is  the  two-fluid 
bichromate  of  potash  cell.  It  is  much  less  powerful  than 
either  Grove's  or  Bunsen's,  but  is  extensively  used  for  tele- 
graphic purposes. 

430.     DanielFs  Cell.  —  In  Daniell's  cell   the  plates  are 
zinc  and  copper.    The  former  is  usually  immersed  in  dilute 
Fig.  382.  sulphuric  acid,  and  the  latter  in  a 

saturated  solution  of  sulphate  of 
copper.  A  convenient  form  of  this 
cell  is  shown  in  Figure  382.  The 
zinc  in  the  form  of  a  rod  is  placed 
inside  of  the  porous  cell,  which  is 
filled  with  dilute  sulphuric  acid. 
The  outer  cell  is  filled  with  the 
solution  of  sulphate  of  copper.  It 
is  made  of  copper,  and  forms  the 
positive  plate  of  the  cell.  Inside 
the  copper  cell  and  near  the  top  is 
a  copper  shelf  perforated  with  holes,  on  which  are  piled  a 
number  of  crystals  of  sulphate  of  copper.  When  the  cell 
is  in  action,  the  hydrogen,  as  it  is  set  free,  is  absorbed  by 


352  NATURAL    PHILOSOPHY. 

the  solution  of  the  sulphate  of  copper  which  it  gradually 
decomposes.  Metallic  copper  is  liberated  from  this  solu- 
tion and  deposited  upon  the  copper,  while  the  zinc  is  grad- 
ually consumed  by  the  sulphuric  acid  in  the  porous  cup. 
As  the  solution  of  sulphate  of  copper  gets  weaker,  a  fresh 
portion  of  the  sulphate  is  dissolved  from  the  shelf.  The 
power  of  this  cell  steadily  decreases  till  the  dilute  acid  in 
the  porous  cup  is  saturated  with  sulphate  of  zinc,  after 
which  it  remains  constant  for  a  very  long  time. 

431.    Gravity  Cells.  —  In  gravity  cells  the  plates  are  placed 
horizontally,  and  the  liquids  are  kept  apart  chiefly  by  their  dif- 
Fig.  383.  ference  of  density,  the  denser 

liquid  being  placed  at  the 
bottom.  The  best  form  of 
this  cell,  and  one  which  may 
be  taken  as  the  type  of  all 
the  others,  is  Thomson's  tray 
cell  (Figure  383). 

In  every  form  of  Daniell's 
cell  the  sulphate  of  copper 
ultimately  finds  its  way  to 
the  zinc  and  spoils  the  action.  To  retard  this  result  indefi- 
nitely, Sir  William  Thomson  constructed  the  tray  cell.  The  cop- 
per plate  is  placed  horizontally  at  the  bottom  and  covered  with 
a  saturated  solution  of  sulphate  of  zinc.  The  zinc,  in  the  form 
of  a  grating,  is  placed  horizontally  near  the  top  of  the  cell.  A 
glass  tube  is  placed  vertically  in  the  solution  with  its  lower  end 
just  above  the  surface  of  the  copper  plate.  Crystals  of  sulphate 
of  copper  are  dropped  down  this  tube.  These  crystals  dissolve 
in  the  liquid,  and  form  a  solution  of  greater  density  than  that  of 
the  sulphate  of  zinc  alone,  so  that  it  cannot  get  at  the  zinc 
except  by  diffusion.  To  retard  this  process  of  diffusion,  a 
siphon,  consisting  of  a  glass  tube  stuffed  with  cotton  wick,  is 
placed  with  one  end  midway  between  the  zinc  and  copper  and 
with  the  other  end  in  a  vessel  outside,  so  that  the  liquid  is  very 
slowly  drawn  off  near  the  middle  of  its  depth.  To  supply  the 
place  of  this  liquid,  water,  or  a  weak  solution  of  sulphate  of 


NATURAL    PHILOSOPHY. 


353 


zinc  is  added  above,  as  required.  In  this  way  the  greater  part 
of  the  sulphate  of  copper,  rising  through  the  liquid  by  diffusion, 
is  drawn  off  by  the  siphon  before  it  reaches  the  zinc,  and  the 
zinc  is  surrounded  by  a  liquid  nearly  free  from  sulphate  of 
copper. 

432.  Ledanche   Cell.  —  This   cell  consists  of   zinc   and 
carbon  separated  by  a  porous  cup  (Figure  384).     The  zinc 
is  surrounded  by  a   solution  Fig.  384. 

of  sal-ammoniac,  and  the  car- 
bon by  a  mixture  of  black 
oxide  of  manganese  and  pow- 
dered carbon.  The  cell  con- 
taining the  powder  is  filled  up 
with  water.  This  cell  has 
small  power,  but  for  discon- 
tinuous work  will  remain  in 
action  for  years,  without  any 
other  attention  than  occasion- 
ally filling  up  the  cell  with  £ 
water. 

433.  The    Voltaic  Battery. 
—  The    voltaic   battery   is    a 
combination  of  voltaic  cells. 

When  the  poles  of  a  cell  are  not  connected,  they  have  a 
certain  difference  of  potential,  which  is  nearly  constant  for 
each  kind  of  cell,  but  varies  with  the  different  kinds  of 
cells.  When  a  greater  difference  of  potential  is  required, 
it  may  be  obtained  by  connecting  a  number  of  similar  cells 
in  series,  that  is,  connecting  the  positive  pole  of  one  cell 
with  the  negative  pole  of  the  next ;  and  so  on.  All  the 
poles  are  thus  connected  two  by  two,  except  in  the  end 
cells.  The  free  positive  and  negative  poles  of  these  two 
cells  are  the  positive  and  negative  poles  of  the  battery. 

The  difference  of  potential   between   the  poles  of  the 
battery  is   as  many  times  that  between  the  poles  of  the 


354  NATURAL    PHILOSOPHY. 

cell  as  there  ire  cells  in  the  battery.  In  a  battery  of  4 
cells,  if  we  b  oppose  the  difference  of  potential  between 
two  poles  of  the  same  cell  to  be  represented  by  the  num- 
ber 10,  that  between  the  poles  of  the  battery  will  be  repre- 
sented by  40  ;  if  there  are  5  cells,  by  50 ;  and  so  on. 

For  let  us  suppose  that  the  negative  pole  of  the  end 
cell  is  connected  to  the  earth  ;  its  potential  is  zero.  The 
potential  of  the  positive  pole  will  then  be  10.  But  the 
positive  pole  of  the  first  cell  is  in  metallic  communication 
with  the  negative  pole  of  the  second,  and  so  their  poten- 
tials are  equal,  and  therefore  the  potential  of  the  negative 
pole  of  the  second  cell  is  10.  But  the  common  difference 
of  potential  being  10,  the  positive  pole  of  the  second  cell 
has  a  potential  of  20.  This  is  in  metallic  communication 
with  the  negative  pole  of  the  third  cell,  and  therefore  the 
potential  of  the  positive  pole  of  that  cell  is  30,  and  that  of 
the  positive  pole  of  the  fourth  cell  40,  or  the  difference 
between  the  potentials  of  the  poles  of  the  4-cell  battery  is 
40,  or  four  times  the  difference  between  the  poles  of  each 
cell. 

In  electrical  diagrams  a  battery  is  usually  represented 
by  a  series  of  long  and  thin  lines  and  of  short  and  thick 
lines.  The  long  line  at  one  end  represents  the  positive 
pole  of  the  battery ;  and  the  short  line  at  the  other  end, 
the  negative  pole  (Figure  385). 

Fig.  385-  Fig.  386. 


434.  Different  Ways  of  arranging  the  Battery.  —  The 
electromotive  force  of  a  battery  depends  solely  upon  the 
number  of  cells  connected  in  series,  and  not  at  all  upon 
the  size  of  the  plates.  As  the  electricity  has  to  pass 


NATURAL   PHILOSOPHY.  355 

through  the  battery  as  well  as  through  the  wire,  the  battery 
forms  part  of  the  circuit.  Now  the  quantity  of  electricity 
which  flows  through  a  circuit  depends  upon  both  the  elec- 
tromotive force  and  the  resistance.  The  greater  the  former 
and  the  less  the  latter,  the  greater  the  quantity  of  the 
current.  The  larger  the  plates  of  the  cell,  the  less  the 
resistance  of  the  battery.  Hence,  with  the  same  number 
of  cells  in  series,  the  larger  the  plates  the  greater  the 
quantity  of  the  current  which  the  battery  will  give. 


Instead  of  using  cells  with  larger  plates,  the  cells  are 
usually  connected  side  by  side,  as  shown  in  Figure  386. 
The  effect  of  connecting  cells  side  by  side  is  not  to  increase 
the  electromotive  force  of  the  battery,  but  to  diminish  its 
resistance,  and  so  to  increase  the  quantity  of  the  current. 
In  Figure  387  twenty  cells  are  represented  as  connected 
in  series.  Both  the  electromotive  force  and  the  resistance 
of  this  battery  are  20  times  those  of  a  single  cell  of  the  kind 
employed  in  the  battery. 

Fig.  388. 


In  Figure  388,  twenty  cells  are  represented  as  connected 
side  by  side.  The  electromotive  force  of  this  battery  is 
that  of  one  cell  only,  but  its  resistance  is  only  ^  of  that 
of  one  cell. 

In  Figure  389,  twenty  cells  are  represented  as  connected 
in  a  way  intermediate  between  the  last  two  cases.  First 


356  NATURAL    PHILOSOPHY. 

they  are   arranged   in  series  of   5  each,  forming  4   com- 
pound  cells,  which   are  connected   side    by   side.       The 

electromotive  force  of 
this  battery  is  5  times 
that  of  a  single  cell,  and 
its  resistance  is  £  the 
resistance  of  a  single 
cell. 

A  battery  gives  its 
maximum  current  when  its  cells  are  so  connected  that 
its  internal  resistance  is  just  equal  to  the  external  resist- 
ance of  the  wire  which  connects  its  poles. 

//.    ELECTROLYSIS. 

435.  Electrolytic  Action.  —  If  two  platinum  wires,  con- 
nected with  the  poles  of  a  battery  in  action,  are  immersed 
in  dilute  sulphuric  acid  (H2SO4),  the  acid  will  be  decom- 
posed. The  hydrogen  will  be  set  free  at  the  wire  connected 
with  the  negative  pole  of  the  battery,  while  oxygen  will 
appear  at  the  other  wire.  This  action  can  be  most  readily 
shown  to  a  class  by  placing  the  dilute  acid  in  a  tank  with 
parallel  glass  sides,  and  throwing  an  image  of  the  wires  in 
the  tank  on  a  screen.  Torrents  of  bubbles  of  gas  will  be 
seen  to  rise  from  the  platinum  wires.  The  decomposition 
of  the  acid  (H,SO4)  into  H.,  and  SO4,  and  the  liberation 
of  these  at  the  two  wires  is  the  work  of  the  electric  current, 
and  is  called  the  electrolytic  action.  The  SO4  set  free  at  the 
positive  wire  attacks  the  water  (H2O),  and,  uniting  with  its 
hydrogen,  forms  H2SO4,  and  sets  the  oxygen  free.  This 
latter  action  is  a  purely  chemical  action,  and  is  called  the 
secondary  action. 

If  a  solution  of  sulphate  of  copper  (CuSO4)  is  used 
instead  of  the  dilute  sulphuric  acid,  copper  is  deposited  on 
the  negative  wire,  while  oxygen  is  set  free  at  the  positive 
wire.  The  electrolytic  action  in  this  case  consists  in  the 


NATURAL    PHILOSOPHY.  357 

separation  of  the  CuSO4  into  Cu  and  SO4,  and  in  the  libera- 
tion of  these  at  the  wires.  The  secondary  action  is  pre- 
cisely the  same  as  before. 

If,  in  the  last  case,  the  wire  connected  with  the  positive 
pole  of  the  battery  is  copper  instead  of  platinum,  no  oxy- 
gen will  be  set  free,  but  the  wire  itself  will  be  gradually 
eaten  away.  The  electrolytic  action  is  the  same  as  before, 
but  in  the  secondary  action  the  SO4  attacks  the  copper 
wire  instead  of  the  water,  and  uniting  with  it  forms  CuSO4 
again,  so  that  the  solution  will  remain  of  the  same  strength, 
while  the  copper  wire  is  consumed. 

436.  Faraday's  Nomenclature  of  Electrolysis.  —  Faraday 
called   the   decomposition   of   a  substance   by   means   of 
electricity,   electrolysis;    the    substance    decomposed,    the 
electrolyte;    the   poles  at  which   the    decomposition    takes 
place,  the  electrodes ;  the  one  connected  with  the  positive 
pole  of  the  battery  the  anode,  and  the  one  connected  with 
the  negative  pole  of  the  battery  the  cathode;  the  products 
of  the  decomposition,  the  ions  ;  the  one  going  to  the  anode 
the  anion,  and  the  one  going  to  the  cathode  the  cation. 

437.  Theory    of    Electrolysis. — Electrolysis    occurs    only 
•while  the  body   is   in   the  liquid  state.     The  free  mobility  of 
the  particles   is  a  necessary  condition  of  electrolysis,  for   the 
process  can  only  take  place  in  one  of  two  ways. 

The  molecule  next  one  of  the  electrodes  is  decomposed.  One 
constituent  of  it  goes  to  the  near  electrode,  and  the  other  either 
travels  to  the  other  electrode  or  combines  with  a  constituent  of 
the  molecule  next  to  it,  setting  free  a  portion  similar  and  equal 
to  itself,  which  in  its  turn  combines  with  the  corresponding 
portion  of  the  molecule  next  to  it,  and  so  on.  In  either  case  the 
free  mobility  of  the  particles  is  an  essential  condition. 

"  Clausius,  who  has  bestowed  much  study  on  the  theory  of 
the  molecular  agitation  of  bodies,  supposes  that  the  molecules 
of  all  bodies  are  in  a  state  of  constant  agitation,  but  that  in  solid 
bodies  each  molecule  never  passes  beyond  a  certain  distance 
from  its  original  position,  whereas  in  fluids  a  molecule,  after 


358  NATURAL   PHILOSOPHY. 

moving  a  certain  distance  from  its  original  position,  is  just  as 
likely  to  move  still  farther  from  it  as  to  move  back  again.  Hence 
the  molecules  of  a  fluid  apparently  at  rest  are  continually  chang- 
ing their  positions,  and  passing  irregularly  from  one  part  of  the 
fluid  to  another.  In  a  compound  fluid  he  supposes  that  not 
only  do  the  compound  molecules  travel  about  in  this  way,  but 
that,  in  the  collisions  which  occur  between  the  compound  mole- 
cules, the  atoms  of  which  they  are  composed  are  often  separated 
and  change  partners,  so  that  the  same  individual  atom  is  at  one 
time  associated  with  one  atom  of  the  opposite  kind  and  at 
another  time  with  another. 

"  This  process  Clausius  supposes  to  go  on  in  the  liquid  at  all 
times  ;  but  when  an  electromotive  force  acts  on  the  liquid,  the 
motions  of  the  molecules,  which  before  were  indifferently  in  all 
directions,  are  now  influenced  by  the  electromotive  force,  so 
that  the  positively  charged  molecules  have  a  greater  tendency 
towards  the  cathode  than  towards  the  anode,  and  the  negatively 
charged  molecules  have  a  greater  tendency  to  move  in  the  oppo- 
site direction.  Hence  the  molecules  of  the  cation  will,  during 
their  intervals  of  freedom,  struggle  towards  the  cathode  ;  but 
will  continually  be  checked  in  their  course  by  pairing  for  a  time 
with  molecules  of  the  anion,  which  are  also  struggling  through 
the  crowd,  but  in  the  opposite  direction." 

The  same  quantity  of  electricity  will  always  produce  the  same 
amount  of  chemical  effect.  If  three  similar  vessels,  A,  ff,  C, 
with  platinum  plates,  and  containing  acidulated  water,  are  ar- 

Fig.  39°. 


ranged  as  in  Figure  390,  and  a  battery  current  passes  through 
them,  the  sum  of  the  quantities  of  gas  produced  in  B  and  C  will 
be  exactly  equal  to  that  produced  in  A. 

438.    The  Voltameter.  —  The  voltameter  is  an  instrument 


NATURAL    PHILOSOPHY.  359 

for  measuring  the  quantity  of  the  current.  It  was  in- 
vented by  Faraday,  and  consists  of  a  dish  filled  with  acid- 
ulated water  and  fitted  with  electrodes,  as  shown  in  Figure 
391.  Receivers  over  the  electrodes  collect  the  gases  as 
they  are  set  free.  The  quantity  of  the  gas  liberated  per 
minute  measures  the  mean  strength  of  the  current  during 
the  time,  and  the  total  quantity  of  the  gas  collected  meas- 
ures the  total  quantity  of  electricity  which  has  passed 
through  the  circuit.  It  is  necessary  to  collect  the  gases 

Fig.  39'- 


separately,  as  chemically  clean  platinum  has  the  power  to 
cause  the  hydrogen  and  oxygen  to  reunite.  The  receiving 
tubes  are  first  filled  with  water  and  inverted  over  the  elec- 
trodes. As  the  gas  rises  it  displaces  the  water.  The 
receivers  are  graduated  so  as  to  show  the  amount  of  the 
gas  collected. 

439.  Electro-Metallurgy,  —  Whenever  solutions  of  com- 
pounds of  metals  are  decomposed,  the  metal  is  deposited 
upon  the  cathode.     This  deposition  of  metals  by  means 
of   the  electric   current  is   called  electro-metallurgy.     This 
process  is  of  great  practical  importance.     The   two  chief 
processes  of  electro-metallurgy  are  electrotyping  and  electro- 
plating. .The  former  is  copying  by  means  of  electricity, 
and  the  latter  is  coating  the  baser  metals  with  the  more 
noble  by  means  of  electricity. 

440.  Electrotyping. —  Anything  maybe  electrotyped  of 


360  NATURAL    PHILOSOPHY. 

which  a  mould  may  be  taken  in  wax.  The  chief  use  of 
electrotyping  is  in  copying  the  face  of  printers'  type  and 
wood-engravings,  after  they  have  been  arranged  for  the 
pages  of  a  book. 

A  mould  is  first  taken  in  wax  of  the  article  to  be  copied. 
The  face  of  this  mould  is  coated  with  a  thin  film  of  some 
conducting  substance,  such  as  graphite  powder.  The 
mould  is  then  hung  up  in  a  trough  filled  with  a  solution  of 
sulphate  of  copper,  called  the  bath.  The  mould  is  connected 
with  the  negative  pole  of  the  battery,  so  as  to  make  it  a 
cathode.  A  plate  of  copper  is  hung  in  the  bath  opposite 
the  mould,  and  connected  with  the  positive  pole  of  the  bat- 
tery, so  as  to  make  it  an  anode.  On  the  passage  of  the 
current  through  the  bath,  copper  is  deposited  from  the 
solution  upon  the  mould  in  a  uniform  coherent  sheet, 
while  the  anode  is  gradually  eaten  away  by  the  secondary 
action.  This  secondary  action  keeps  the  bath  of  uniform 
strength.  The  moulds  are  usually  hung  in  the  bath  at 
night,  and  in  the  morning  they  are  removed,  and  the  wax 
melted  off.  The  copper  casts  are  made  sufficiently  firm 
for  use  in  printing  by  backing  them  with  type-metal. 

441.  Electroplating.  —  The  ordinary  table-ware,  such  as 
knives,  forks,  tea-sets,  etc.,  is  plated  with  silver  by  elec- 
trolysis. The  article  to  be  plated  is  first  very  carefully 
cleaned,  and  then  hung  up  in  a  bath  containing  a  solution 
of  cyanide  of  silver.  It  is  then  connected  with  the  nega- 
tive pole  of  a  battery,  while  a  piece  of  silver  hung  in  front 
of  it  is  connected  with  the  positive  pole.  On  the  passage 
of  the  current,  silver  is  deposited  from  the  solution  upon 
the  article  which  forms  the  cathode,  while  the  silver  of  the 
anode  is  gradually  eaten  away  by  the  secondary  action. 
As  before,  the  secondary  action  keeps  the  solution  of 
uniform  strength.  If  the  article  is  thoroughly  cleaned,  and 
the  current  is  maintained  at  the  right  strength,  the  silver 
will  be  deposited  uniformly  over  its  surface,  and  will  adhere 
firmly  to  it. 


NATURAL   PHILOSOPHY.  361 

When  the  article  is  to  be  gilded,  or  coated  with  gold,  the 
bath  must  contain  a  solution  of  the  cyanide  of  gold,  and 
the  anode  must  be  of  gold.  In  other  respects  the  process 
is  the  same  as  in  silver-plating. 

In  nickel-plating  the  bath  contains  a  solution  of  some 
compound  of  nickel,  and  the  anode  is  a  piece  of  nickel. 

442.  Electrolytic  Polarization.  —  When  the  battery  used  is 
too  weak  to  decompose  the  electrolyte,  a  state  of  polarisation  or 
strain  is  set  up,  which  very  closely  resembles  that  set  up  in  a 
Leyden  jar.     Electrolytic  polarization  may  be  compared  to  the 
ordinary  charging  of  a  Leyden  jar,  and  electrolytic  decomposi- 
tion to  the  case  in  which  the  charge  is  strong  enough  to  per- 
forate the  glass. 

443.  Secondary  Batteries.  —  When  a  current  is  sent  through 
a  voltameter  for  a  considerable  time,  the  plates  acquire  some 
sort  of  electrical  polarization,  such  that,  if  the  battery  is  removed 
and  the  plates  connected  by  a  wire,  a  current  will  be  observed 
in  the  wire  in  the  reverse  direction  to  that  of  the  battery  cur- 
rent.    When  the  plates  of  the  voltameter  are  made  very  large, 
it  takes  a  longer  time  to  polarize  the  plates,  but  the  reversed  or 
"  secondary "  current  is  extremely  powerful.     The   secondary 
current  lasts  only  a  short  time,  but  its  total  energy  is  equal  to 
the  total  energy  which  it  has  received  from  the  battery  in  a  long 
time,  and  therefore,  during  the  time  which  it  lasts,  the  second- 
ary current  will  be  much  stronger  than  the  "  primary  "  or  battery 
current. 

Fig.  392. 


Advantage  has  been  taken  of  this  fact  in  the  construction  of 
secondary  batteries,  which  enable  us  with  two  or  three  cells  of 
Grove  or  Bunsen  to  obtain,  for  a  short  time,  effects  equal  to 
those  which  could  be  obtained  directly  only  by  the  use  of  many 


NATURAL   PHILOSOPHY. 


hundred  cells.  The  plates  of  these  secondary  batteries  are  of 
lead,  and  the  liquid  is  dilute  sulphuric  acid.  In  order  to  obtain 
currents  of  high  potential,  a  number  of  secondary  elements  are 

Fig-  393- 


arranged  "side  by  side  "  and  charged,  and  then  are  connected 
"in  series."  While  the  elements  are  being  charged  they  are 
arranged  as  in  Figure  392. 

The  connections  are  then  altered  to  the  arrangement  of 
Figure  393,  when  the  differences  of  potential  given  to  each 
element  separately  are  all  added  together,  and  produce  a  great 
difference  of  potential  at  the  ends  of  the  battery. 


444. 


D.   ELECTRO-MAGNETIC  INDUCTION. 
An   Electric    Whirl  constitutes   a   Magnet.  —  If   a 


current  of  electricity  is  sent  round  a  wire  bent  in  the  form 
of  a  ring  (Figure  394),  the  ring  will  act  in  all 
respects  like  a  short  magnet.  The  left-hand 
side  of  the  ring  to  a  person  swimming  round 
it,  with  the  current  and  with  his  face  towards 
the  centre  of  the  ring,  will  be  a  north  pole, 
and  the  other  side  of  the  ring  a  south  pole. 
If  the  wire  is  wound  round  and  round  in  the 
form  of  a  coil,  the  multiplication  of  the  rings 
will  produce  a  stronger  magnet.  By  changing  the  strength 
of  the  current  in  such  a  coil,  we  change  the  strength  of  its 
magnetism,  and  by  changing  the  direction  of  the  current 
we  reverse  the  poles  of  the  magnet. 

445.  Electro-Magnet.  —  If  a  bar  of  soft  iron  is  placed 
within  the  axis  of  the  coil,  and  a  current  sent  through 
the  coil,  the  iron  becomes  a  magnet,  with  its  north  pole  to 


NATURAL    PHILOSOPHY.  363 

the  left  hand  of  a  person  swimming  around  the  coil  with 
the  current  and  with  his  face  towards  the  axis  of  the  coil. 
A  wire  coiled  round  a  bar  of  soft  iron  constitutes  an  electro- 
magnet. 

Such  a  magnet  is  active  only  while  the  current  is  passing 
through  its  coil.  It  loses  its  magnetism  the  moment  the 
current  stops.  Its  poles  are  reversed  by  reversing  the  cur- 
rent in  its  coil.  As  the  strength  of  the  current  increases 
the  magnetism  of  the  magnet  increases,  but  less  and  less 
rapidly,  till  it  reaches  a  certain  point,  beyond  which  an 
increase  in  the  strength  of  the  current  produces  no  increase 
of  magnetism.  At  this  point  the  magnet  is  said  to  be 
saturated.  Below  the  point  of  saturation  every  change  in 
the  strength  of  the  current,  however  slight,  produces  a 
corresponding  change  of  magnetism. 

Electro-magnets  are  usually  made  of  the  horseshoe 
form  (Figure  395),  and  they  are  Fig. 

much  stronger  than  the  ordinary 
^teel  magnets.  The  iron  core  of 
each  coil  is  often  a  separate  bar, 
and  the  two  bars  are  connected  by 
a  straight  bar  at  the  base. 

446.  Magneto- Electric  Currents.  —  If  a  wire  is  moved  in 
the  neighborhood  of  a  magnet  in  any  direction  whatever, 
except  along  a  line  of  magnetic  force,  a  difference  of  poten- 
tial will  be  produced  at  the  ends  of  the  wire  which  would 
cause  a  current  to  flow  through  a  wire  connecting  the  ends 
and  not  acted  on  inductively  by  the  magnet.  If  a  person 
carries  a  wire  in  front  of  him  in  any  direction  whatever 
with  reference  to  the  north  pole  of  a  magnet,  the  left-hand 
end  of  the  wire  will  be  brought  to  a  higher  potential.  It 
is  the  reverse  when  the  wire  is  moved  about  the  south  pole 
of  the  magnet. 

If  a  magnetic  pole  is  moved  in  the  neighborhood  of  a 
wire,  in  any  direction  except  parallel  to  it,  a  current  will 


•  «S-  9R9< 

U. 


364 


NATURAL   PHILOSOPHY. 


be  induced  in  the  wire.     If,  for  instance,  a  magnet  NS 
Fig.  396.  (Figure  396)  is  moved  suddenly 

in  or  out  of  the  coil  of  wire,  a 
current  will  be  induced  in  the 
coil,  which  will  be  in  one  direc- 
tion on  inserting  the  pole,  and  in 
the  other  on  withdrawing  it.  Jf 
the  magnet  is  reversed  so  as  to 
use  the  other  pole,  the  current 
will  be  reversed. 

If  a  coil  of  wire  through  which 
a  current  is  passing  is  used  instead  of  a  steel  magnet 
(Figure  397),  precisely  similar  results  are  obtained.  The 
more  suddenly  the  steel  magnet  or  the  coil  conveying  a 
current  is  moved  in  or  out  of  the  coil,  the  stronger  the 
current  induced. 

Fig.  397- 


If  the  small  coil  is  left  within  the  larger  coil,  any  change 
whatever  in  the  current  in  the  inner  coil,  whether  of 
strength  or  direction,  will  develop  a  current  by  induction 
in  the  outer  coil.  So,  too,  if  any  two  coils  of  wire,  through 
one  of  which  a  current  is  passing,  are  near  together,  any 
movement  of  the  coils  with  respect  to  each  other,  or  any 
change  in  the  current  in  the  first,  will  induce  a  current 
in  the  second. 

If  a  bar  of  soft  iron  is  inserted  in  the  inner  coil  of  Fig- 


NATURAL    PHILOSOPHY. 


ure  397,  the  current  induced  in  the  outer  coil,  either  by 
motion  or  change  of  current,  will  be  very  much  stronger. 
The  same  is  true  to  a  less  extent  when  a  bar  of  any  other 
metal  is  inserted  in  the  inner  coil. 


Fig.  398. 


447.  The  Bell  Telephone.  —  Figures  398  and  399  show 
the  sending  and  receiving  instrument  of  the  Bell  telephone, 
in  section  and  perspective.  It  Fig.  399. 

consists  of  a  steel  magnet  M 
around  one  end  of  which  is  wound 
a  coil  of  fine  wire  B.  The  coil 
and  magnet  are  enclosed  in  a 
wooden  case,  which  serves  as 
a  handle.  One  end  of  this  case 
is  considerably  larger  than  the 
magnet,  and  is  hollowed  out  at 
E,  so  as  to  serve  as  a  mouth- 
piece or  an  ear-piece.  A  dia- 
phragm of  thin  iron  D  is 
stretched  across  the  wide  end  of 
the  case,  just  in  front  of  the  pole 
of  the  magnet,  which  it  does  not 
touch. 

The  transmitting  and  receiving 
instruments,  which  are  exactly 
alike  in  construction,  are  con- 
nected together  by  a  wire.  On  speaking  into  the  mouth- 


366  NATURAL   PHILOSOPHY. 

piece,  the  air  in  it  is  thrown  into  vibrations,  and  these  vibra- 
tions are  communicated  to  the  diaphragm.  The  vibrations 
of  the  iron  plate  produce  slight  temporary  alterations  in  the 
magnetism  of  the  steel  magnet.  These  changes  of  mag- 
netism in  the  magnet  induce  corresponding  currents  in  the 
wire  of  the  coil,  which  are  transmitted  over  the  wire  which 
connects  the  two  instruments.  Hence  pulsations  of  elec- 
tricity exactly  corresponding  to  the  vibrations  of  the  dia- 
phragm of  the  first  instrument  will  be  transmitted  over 
the  wire  and  through  the  coil  of  the  receiving  instrument. 
These  pulsations  of  the  current  in  the  coil  will  induce  in 
the  magnet  of  the  receiving  instrument  exactly  the  same 
changes  of  magnetism  as  those  by  which  they  were  pro- 
duced in  the  sending  instrument.  These  changes  of  mag- 
netism cause  the  magnet  to  pull  upon  the  iron  plate  in 
front  of  it  with  a  varying  force,  and,  consequently,  to  make 
it  vibrate  exactly  like  the  diaphragm  of  the  transmitter. 
These  vibrations  are  communicated  to  the  air,  and  then  to 
the  ear  of  the  operator,  which  is  placed  at  the  mouth  of 
the  receiver.  The  words  spoken  into  the  transmitter  are 
thus  reproduced  in  the  receiver. 

Figure  400  shows  the  way  in  which  the  two  instruments 

Fig.  400. 


a  a 


4oi. 

tf£ 

I 
|W 

±  -  ' 


NATURAL    PHILOSOPHY.  367 

are  connected.  The  wire  at  each  end  is  connected  with 
the  earth  by  means  of  a  copper  plate  sunk  in  the  ground, 
so  that  the  circuit  is  completed  by  the  earth.  Otherwise 
two  wires  must  be  used  between  the  instruments. 

The  Bell  telephone  is  a  beautiful  illustration  of  the  two 
aspects  of  electro-magnetic  induction. 

448.  The  Edison  Telephone.  —  In  the  Bell  telephone  no 
battery  is  used.  In  the  Edison  telephone  a  battery  is 
used,  and  a  current  transmitted  from  the  battery  is  thrown 
into  undulations  by  an  arrangement  called  the  carbon  but- 
ton. This  button  is  shown  in  Figure  401.  Fig.  4oi. 
b  is  a  disc  or  button  of  carbon,  in  the  form 
of  compressed  lampblack  ;  a  and  c  are 
metallic  plates  placed  against  the  front 
and  back  of  the  disc  of  carbon.  One  of 
the  poles  of  the  battery  B  is  connected 
with  a,  and  the  other  with  c.  The  cur- 
rent is  obliged  to  pass  from  the  plate  a  to  c  through  the 
carbon  disc.  An  increase  of  pressure  upon  the  metallic 
plates  a  and  c  diminishes  the  resistance  of  the  button, 
either  by  increasing  the  density  of  the  carbon  disc  or  by 
improving  the  contact  between  the  plates  and  the  disc. 
The  button  is  exceedingly  sensitive  to  variations  of  pressure, 
the  slightest  alteration  of.  pressure  producing  a  change  in 
the  strength  of  the  current  which  traverses  the  carbon. 

One  form  of  the  Edison  transmitter  is  shown  in  Figure 
402.  The  mouth-piece  is  of  vulcanite.  Back  of  this  is 
the  vibrating  disc,  and  behind  this  is  a  little  hemispherical 
button  of  aluminium.  This  button  rests  upon  the  metallic 
plate  in  front  of  the  carbon  disc.  This  plate  is  of  plati- 
num. Behind  the  carbon  disc  is  a  second  platinum  plate, 
held  in  position  by  means  of  the  screw  at  the  back  of  the 
instrument.  The  battery  wires  are  connected  with  the  two 
platinum  plates  in  such  a  way  that  the  current  must  traverse 
the  carbon  disc. 


368  NATURAL   PHILOSOPHY. 

On  speaking  into  the  mouth-piece,  the  disc  is  thrown  into 
vibration.  These  vibrations  are  communicated  to  the  plati- 
num plate  and  the  carbon  disc  by  means  of  the  aluminium 
button,  thus  producing  undulations  in  the  current  exactly 
corresponding  to  the  vibrations  of  the  disc  at  the  bottom 
of  the  mouth-piece. 

Fig.  402. 


The  receiving  instrument  of  the  Edison  telephone  is 
similar  to  that  of  the  Bell  telephone.  Changes  of  magnet- 
ism are  induced  in  it  by  the  undulating  current  which  trav- 
erses its  coil,  and  these  changes  of  magnetism  cause  the 
disc  in  front  of  the  magnet  to  vibrate  exactly  like  that  of 
the  transmitter. 

449.  The  Induction  Coil.  —  The  induction  coil  consists  of 
two  coils :  an  inner  or  primary  coil    of  coarse  wire,  en- 
closing pieces  of  soft  iron,  usually  in  the  form  of  wires  ; 
and  an  outer  or  secondary  coil  of  fine  wire.     The  coils  are 
carefully  insulated  from  each  other.     A  current  of  elec- 
tricity is  sent  through  the  primary  coil,  and  any  change  in 
the  strength  of  this  primary  current  develops  by  induction 
a  current  in  the  secondary  coil.     The  induced  current  is 
much  less  in  quantity  than  the  primary  current,  but  it  has 
a  far  greater  electromotive  force. 

450.  The  Use  of  the  Induction  Coil  with  the  Telephone.  — 


NATURAL    PHILOSOPHY. 


369 


Fig.  403. 


It  has  been  found  that  the  induced  currents  from  the  in- 
ductive coil  are  better  adapted  for  working  the  telephone 
than  the  direct  current  from 
the  battery.  Figure  403  shows 
the  way  the  coil  is  used  with 
the  telephone.  b  is  the  car- 
bon disc  of  the  transmitter, 
a  and  c  are  the  platinum  plates, 
B  is  the  battery,  d  is  the  pri- 
mary coil  of  the  induction  coil, 
and  ee  its  secondary  coil.  The 
battery  is  connected  with  the 
plates  a  and  c,  and  with  the  primary  coil  d.  One  end  of  the 
wire  of  the  secondary  coil  is  connected  with  the  earth  by 
the  wire  G ;  and  the  other  end  to  the  line  Z,  which  runs  to 
the  receiving  instrument.  The  undulations  of  the  current 
in  the  primary  coil  induce  corresponding  undulations  of 
greater  electromotive  force  in  Fig.  404. 

the  secondary  coil.  These  lat- 
ter undulations  pass  over  the 
line,  and  work  the  receiving 
instrument. 

451.  The  Electrical  Receiver 
of  the  Photophone.  —  It  has  been 
found  that  the  conducting  power 
of  selenium  and  certain  other  sub- 
stances varies  with  the  intensity 
of  the  light  to  which  they  are  ex- 
posed This  suggested  to  Bell 
the  use  of  these  substances  in 
the  receiver  of  his  photophone. 
In  Figure  404  is  shown  one  of 
the  receiving  cells  employed  by 
Bell.  A  plate  of  glass  is  first 
coated  with  silver.  The  silver  is 
then  scratched  through  in  a  broad 


37° 


NATURAL   PHILOSOPHY. 


zigzag  line,  so  as  to  divide  the  coating  into  two  portions,  as 
shown  in  this  figure.  Interlocking  tongues  project  from  the  two 
portions  like  the  teeth  of  combs.  The  glass  plate  is  then 
smoked  so  as  to  fill  the  spaces  between  the  tongues  with  a  good 
film  of  lampblack.  The  two  silver  combs  are  connected  with 
the  two  poles  of  a  voltaic  battery.  The  current  is  obliged  to 
traverse  the  film  of  lampblack  in  order  to  pass  from  one  comb 
to  the  other.  So  long  as  the  cell  is  exposed  to  light  of  uniform 
intensity  the  current  which  traverses  the  cell  will  be  uniform. 
Any  change  in  the  intensity  of  the  light  upon  the  receiver  alters 
the  resistance  of  the  lampblack  film  and  the  strength  of  the 
current.  When  this  cell  is  used  as  a  receiver,  an  ordinary  tele- 
phone receiver  is  included  in  the  circuit.  As  in  the  case  of  the 
Edison  telephone,  the  sounds  are  louder  when  the  cell  is  in  the 
primary  circuit  of  the  induction  coil,  and  the  telephone  receiver 
in  the  secondary  circuit. 

Fig.  4°s- 


The  selenium  cell  consists  of  a  number  of  discs  of  brass  sep- 
arated by  thin  rings  of  selenium,  as  shown  in  section  in  Figure 
405.  The  two  end  discs  are  connected  with  the  poles  of  a  bat- 
tery, in  the  circuit  of  which  is  also  included  a  telephone  re- 
ceiver. As  before,  it  is  found  better  to  place  the  selenium  cell 
in  the  primary  circuit  of  an  induction  coil,  and  the  telephone 
receiver  in  the  secondary  circuit. 

When  the  selenium  cell  is  used  as  a  receiver,  it  is  placed  in 
the  focus  of  a  parabolic  or  cylindrical  mirror. 

452.  The  Microphone.  —  When  there  is  an  imperfect  con- 
tact at  any  point  of  a  circuit  carrying  a  battery  current,  any 
change  in  the  goodness  of  the  contact  will  produce  a 
change  in  the  strength  of  the  current,  and  cause  a  sound 
in  a  telephone  receiver  included  in  the  circuit.  When  the 
imperfect  contact  is  between  pieces  of  carbon  lightly 


NATURAL    PHILOSOPHY. 


371 


Fig.  406. 


pressed  together,  variations  of  the  current  are  produced  by 
the  slightest  sounds  occurring  near  the  carbons. 

The  microphone  consists  of  three  pieces  of  carbon, 
C,  A,  and  C  (Figure  406).  The  wires  from  the  battery  B 
are  connected  with  the 
pieces  C  and  C  in  such  a 
way  that  all  the  pieces  of 
carbon  are  in  the  circuit. 
The  wires  X  and  Krun  to 
the  receiver  of  a  telephone. 
The  lowest  whisper  spoken 
near  the  microphone  is 
loudly  reproduced  in  the 
telephone.  As  the  carbon 
rod  A  is  thrown  into  vibra- 
tions by  the  pulsations  of  sound,  it  alternately  lengthens 
and  shortens.  These  alterations  of  length  alternately 
improve  and  impair  the  contact  at  C  and  C'. 

To  intensify  the  effect,  the  microphone  is  usually  placed 
on  a  sounding-board  D  (Figure  407).     The  sound  caused 

Fig.  407. 


by  a  fly  walking  on  the  sounding-board  is  distinctly  audi- 
ble at  the  distant  telephone.  The  ticking  of  a  watch  on 
the  sounding-board  sounds  like  the  blows  of  a  hammer. 


372  NATURAL   PHILOSOPHY. 

453.  The  Audiometer.  —  This  instrument  is  shown  in  Fig- 
ure 408.  B  and  C  are  two  coils  of  wire,  exactly  alike,  and 
placed  at  opposite  ends  of  a  rod  divided  into  inches  and  frac- 
tions of  an  inch.  D  is  a  coil  that  may  be  slid  along  this  rod,  E 
is  a  microphone,  and  F\s  a  battery.  The  battery  is  connected 
with  the  microphone,  and  with  the  coils  B  and  C  in  such  a  way 
that  the  current  traverses  them  in  opposite  directions.  The 
sliding  coil  D  is  connected  with  a  telephone  receiver.  A  watch 
is  placed  upon  the  microphone,  which  must  be  in  a  distant  room, 
so  that  the  ticking  of  the  watch  cannot  be  heard  directly.  The 
undulations  in  the  current  produced  by  the  microphone,  as  they 
traverse  the  coils  B  and  C,  induce  similar  undulations  in  the  coil 
/?,  but  the  undulations  induced  by  B  will  be  in  opposite  direc- 
tions to  those  induced  by  C.  When  the  coil  D  is  at  the  centre 
of  the  rod,  the  two  sets  of  undulations  induced  in  it  will  be  equal 
and  will  neutralize  each  other,  and  no  sound  will  be  heard  at  the 
telephone.  As  D  is  moved  away  from  the  centre,  one  set  of 
induced  undulations  will  begin  to  exceed  the  other,  and  a  sound 
will  begin  to  be  produced  at  the  telephone,  feeble  at  first,  but 
becoming  more  and  more  intense  as  D  is  moved  farther  and  far- 
ther from  the  centre,  and  reaching  a  maximum  when  D  is  moved 
up  close  to  either  B  or  C. 

The  acuteness  of  one's  hearing  may  be  tested  by  noticing  at 
what  point  the  ticking  of  the  watch  becomes  inaudible  at  the  tele- 
phone as  D  is  moved  slowly  towards  the  centre  of  the  rod.  On 
testing  both  ears  in  succession,  it  will  often  be  found  that  one  ear 
hears  better  than  the  other. 

454.  The  Induction  Balance.  —  The  induction  balance  (Fig- 
ure 409)  differs  from  the  audiometer  in  having  two  sliding  coils 
instead  of  one.  The  end  coils  G  and  G'  are  connected  with  the 
microphone  and  battery  as  before,  and  the  sliding  coils  //and  H' 
are  connected  with  the  telephone  receiver  so  that  the  currents 
from  them  shall  traverse  the  telephone  in  opposite  directions. 
The  sliding  coils  //and  H'  are  first  placed  equally  distant  from 
the  end  coils  G  and  G'.  The  two  induced  currents  are  now  ex- 
actly balanced,  and  no  sound  is  heard  at  the  telephone,  as  the 
undulations  from  H  exactly  neutralize  those  from  H'.  If  a  piece 
of  metal,  as  a  small  coin,  is  slid  into  one  of  the  end  coils,  as  G, 
the  balance  of  the  induced  currents  is  at  once  destroyed,  and 


NATURAL   PHILOSOPHY. 


373 


374 


NATURAL   PHILOSOPHY. 


NATURAL   PHILOSOPHY.  375 

the  ticking  of  the  watch  becomes  audible  at  the  telephone.  This 
is  because  the  presence  of  the  metal  in  the  axis  of  the  coil  im- 
proves the  induction  of  the  coil.  If  two  pieces  of  metal,  exactly 
alike  in  every  respect,  are  placed  in  exactly  corresponding  posi- 
tions in  both  the  end  coils,  the  balance  is  again  restored,  and 
the  ticking  of  the  watch  is  again  inaudible  at  the  telephone. 
If,  however,  there  is  the  slightest  difference  in  the  weight  or 
purity  of  the  two  pieces  of  metals,  the  equality  of  the  induced 
current  is  again  destroyed,  and  the  ticking  of  the  watch  is -again 
heard  at  the  telephone. 

This  instrument  may  be  used  for  testing  the  fineness  of  al- 
loys. An  alloy  of  gold  and  silver,  containing  only  two  ounces 
of  gold  to  the  pound  of  silver,  can  be  clearly  distinguished  from 
pure  silver  by  means  of  the  balance.  It  may  also  be  used  for 
detecting  bad  coin. 

The  telephone,  microphone,  audiometer,  and  induction  bal- 
ance furnish  the  most  beautiful  and  complete  illustration  of  the 
different  aspects  of  electro-magnetic  induction. 

Fig.  410. 


455.  Large  Induction  Coils.  —  Figure  410  shows  an  induc- 
tion coil,  capable  of  giving  a  1 7-inch  spark  in  air.  Mr.  Spot- 
tiswoode's  great  coil  (the  most  powerful  ever  constructed)  is 
capable  of  giving  a  spark  in  air  42 y2  inches  long.  The  power  of 
the  coil  depends  in  great  measure  upon  the  length  and  fineness 
of  the  wire  in  the  secondary  coil.  In  the  17-inch  coil  the  wire 
in  the  secondary  coil  is  22  miles  in  length,  while  in  the  Spottis- 


376  NATURAL   PHILOSOPHY. 

woode  coil  it  is  no  less  than  280  miles  long.  A  good  deal  also 
depends  upon  the  quality  of  the  insulation  between  the  primary 
and  secondary  coils  and  between  the  different  layers  of  the  second- 
ary coil.  When  the  current  is  started  or  stopped  in  the  primary 
coil,  the  sudden  change  of  magnetism  in  the  coil  and  its  iron  core 
produces  a  great  difference  of  potential  at  the  ends  of  the  wire 
of  the  outer  coil.  The  more  sudden  the  change  of  magnetism, 
the  greater  the  difference  of  potential  at  the  ends  of  the  sec- 
ondary wire.  It  is  found  that  this  difference  of  potential  is 
greater  on  stopping  the  current  than  on  starting  it.  It  would 
seem  that  the  iron  loses  its  magnetism  more  quickly  than  it 
gains  it. 

That  the  destruction  of  magnetism  may  be  as  sudden  as  pos- 
sible, it  is  found  necessary  to  use  a  bundle  of  fine  wires  for  the 
core  of  the  primary  coil,  instead  of  a  single  rod  of  iron.  The 
wire  will  lose  its  magnetism  much  more  quickly  than  a  single 
rod. 

The  current  is  started  and  stopped  by  means  of  what  is  called 
a  contact-breaker.     The  form  of  contact-breaker  used  for  small 
coils  (up  to  17  inches)  is  called  the  -vibrator.     It  is  shown  in 
Figure  41 1.     It  consists  of  a  vertical  brass  or  steel  spring,  hav- 
Pig  4II  ing  upon  its  upper  end,  in  front, 

a  piece  of  soft  iron  facing  the 
core  of  the  primary  coil,  but  not 
quite  touching  it  ;  and  behind, 
just  opposite  the  soft  iron,  a 
platinum  point,  which  presses 
against  a  second  platinum 
point,  supported  on  a  vertical 
post.  The  wires  from  the  bat- 
tery are  connected  with  the 
spring  and  the  rear  platinum 
point  in  such  a  way  that,  when 
the  current  passes  at  all,  it 
must  pass  from  one  platinum 
point  to  the  other.  The  circuit  is  closed  and  the  current  started 
when  the  points  are  in  contact,  and  it  is  opened  and  the  current 
stopped  when  the  points  are  separated.  The  elasticity  of  the 
spring  tends  to  bring  the  points  together  ;  but  when  the  cur- 


NATURAL   PHILOSOPHY.  377 

rent  starts,  the  core  of  the  primary  coil  becomes  magnetic,  at- 
tracts the  piece  of  soft  iron,  and,  pulling  the  spring  forward, 
separates  the  platinum  points,  and  stops  the  current.  The  core 
then  loses  its  magnetism,  the  iron  is  released,  and  (Tie  spring 
flies  back,  and  brings  the  platinum  points  in  contact  again.  The 
current  starts  again,  the  core  becomes  magnetic,  and  the  points 
are  again  drawn  apart,  and  so  on. 

All  the  experiments  with  vacuum  tubes  succeed  better  with 
a  large  induction  coil  than  with  the  Holtz  machine. 

456.  The  Extra  Current.  —  If  a  current  is  sent  through  a 
coil  of  wire,  the  current  does  not  instantly  reach  its  maximum 
value  when  the  circuit  is  closed,  and  it  does  not  instantly  fall  to 
zero  when  the  circuit  is  broken.     This  effect  is  the  same  as 
would  be  produced  if,  at  the  moment  of  closing,  a  transient  cur- 
rent were  produced  in  the  wire  in  the  opposite  direction  to  the 
primary,  and.  at  the  moment  of  opening,  another  in  the  same 
direction  as  the  primary. 

The  transient  currents  in  a  coil  are  produced  by  the  induc- 
tion of  each  portion  of  the  current  on  the  neighboring  wires,  on 
•winch  it  acts  as  if  they  were  portions  of  another  circuit. 

These  transient  currents  are  called  the  extra  currents  of 
closing  and  opening,  respectively.  If  the  coil  is  unwound  and 
stretched  out,  so  that  no  part  is  near  any  other  part,  except  at 
right  angles  to  it,  the  extra  currents  almost  entirely  disappear. 
For  two  wires  to  act  inductively  on  each  other,  it  is  necessary 
that  they  should  be  near  together,  and  not  at  right  angles. 

457.  The  Condenser  of  the  Induction  Coil.  —  This  is  a  very- 
important  portion  of  an  induction  coil.     It  consists  of  a  number 
of  sheets  of  tin-foil  separated  by  mica,  gutta-percha,  or  paraffined 
paper.     The   1st,  3d,  5th,  7th,  etc.  sheets  are  connected  to  one 
end  of  the  primary  wire  ;  the  2d,  4th,  6th,  8th,  etc.,  to  the  other 
end.     When  the  circuit  is  broken,  the  extra  current,  induced  in 
the  primary  wire  by  breaking,  is  in  the  same  direction  as  the 
primary  current,  and.  therefore  tends  to  prolong  the  magnetiza- 
tion of  the  core.     When  a  condenser  is  used,  the  extra  current 
spends  itself  in  charging  it.     The  condenser  then,  instantly  dis- 
charging itself,  sends  a  current  in  the  reverse  direction  round 
the  core,  and  at  once  demagnetizes  it.    The  condenser  is  usually 
placed  in  the  base  of  the  coil. 


378  NATURAL    PHILOSOPHY. 

458.  Magneto-Electric  Machines.  —  The  fact  that  electric 
currents  are  produced   in  a  wire  by  any  change  of   mag- 
netism near  it,  or  by  moving  the  wire  in  the  neighborhood 
of  a  magnet,  has  been  utilized  in  the  construction  of  ma- 
chines for  the  development  of  very  powerful  currents  of 
electricity.     These  machines  are  called  magneto-electric  or 
dynamo-electric  machines.     The   former   name    is    applied 
more  especially  to  the  machines  in  which  the  electric  cur- 
rents are  produced  by  changes  of  magnetism,  and  the  latter 
to  those  in  which  the  currents  are  produced  mainly  by  the 
motion  of  wire  in  the  neighborhood  of  magnets.     In  all 
the  dynamo-electric  machines  the  currents  are   produced 
by  revolving  coils  of  wire  between  the  poles  of  powerful 
horseshoe  magnets,   which  are  sometimes  steel  magnets, 
but  usually  electro-magnets. 

When  a  wire  is  carried  around  between  the  poles  of  a 
horseshoe  magnet,  a  current  is  developed  in  it  during  each 
half  of  a  revolution,  and  these  currents  will  be  in  opposite 
Fig.  4I2.  directions.     Let  A   (Figure  412)  repre- 

sent the  cross-section  of  a  wire  moving 
around  between  the  poles  W,  S,  in  the 
direction  indicated  by  the  arrow.  When 
on  the  right-hand  side  of  the  vertical 
line  E  E,  the  wire  will  be  crossing  the 
lines  of  magnetic  force  in  one  direction,  and  when  on  the 
left  of  this  vertical,  in  the  opposite  direction.  According 
to  the  rule  already  given,  while  the  wire  is  on  the  right  of 
the  vertical  line,  the  back  end  of  it  will  be  at  a  high  poten- 
tial and  the  front  end  of  it  at  a  low  potential.  This  will 
be  reversed  when  the  wire  is  on  the  left  of  the  vertical 
line.  All  modern  magneto-electric  '  machines  are  con- 
structed on  one  of  two  types,  namely,  that  of  the  Gramme 
machine,  and  that  of  the  Siemens  machine. 

459.  The    Gramme    Machine,  —  The    construction   of    the 
Gramme  machine  and  the  principle  of  its  action  may  be  ex- 


NATURAL   PHILOSOPHY.  379 

plained  by  means  of  the  diagram  given  in  Figure  413.  A  ring 
of  soft  iron,  M  N'  M' S',  is  wound  with  a  copper  wire,  whose 
ends  are  soldered  together  so  as  to  form  a  continuous  conductor. 
This  ring  is  arranged  so  that  it  may  be  revolved  on  a  horizontal 
axis  between  the  poles,  N,  S,  of  a  permanent  magnet  The 
parts  of  the  ring  N'  and  S'  are  rendered  a  north  and  a  south 
pole  by  induction.  As  the  ring  revolves,  these  poles  remain  in 
the  same  position  with  reference  to  the  poles  N  and  S  of  the 
permanent  magnet,  but  not  in  the  same  part  of  the  ring  itself. 
As  the  ring  passes  the  poles  of  the  permanent  magnet,  the  soft 
iron  becomes  magnetized  and  demagnetized  by  induction.  This 


change  of  magnetism  in  the  iron  of  the  ring  produces  a  current 
in  each  element  of  the  coil  of  copper  wire  in  the  neighborhood 
of  the  change.  Also  the  movement  of  these  elements  past  the 
poles  of  the  permanent  magnet  produces  currents  in  them,  and 
these  currents  will  have  the  same  direction  as  those  produced 
by  the  change  of  magnetism.  The  currents  produced  in  all  the 
elements  of  the  coil  above  the  line  MM'  will  be  in  one  direction 
and  will  tend  to  combine  in  one  current.  The  currents  produced 
in  all  the  elements  of  the  coll  below  the  line  MM'  will  be  in  the 
opposite  direction  to  those  above  the  line,  and  these  will  also 
tend  to  unite  in  one  current.  There  is  then  a  tendency  in  the 
upper  half  of  the  ring  to  produce  a  current  in  one  direction,  and 
an  equal  tendency  in  the  lower  half  of  the  Fi 

ring  in  the  opposite  direction.     The  two  , 

halves  of  the  coil  are  now  in  the  condition        |     * 
of  two  batteries  shown  in   Figure  414.     If 
the  points  A  and  B  are  connected  by  a 
wire,  a  current  will  flow  through  the  con- 


380  NATURAL   PHILOSOPHY. 

necting  wire  having  the  electromotive  force  of  either  battery 
and  of  the  quantity  of  both.  In  a  similar  way,  if  the  points  of 
the  coil  M  and  M'  were  connected  by  a  wire,  a  current  would 
flow  through  this  connecting  wire  from  the  point  of  higher 
potential  to  that  of  lower  potential.  Whether  M  or  M'  be  of 
the  higher  potential  depends  upon  the  direction  in  which  the 
ring  revolves.  The  points  M  and  M'  might  be  connected  by 
removing  the  insulating  coating  from  a  little  strip  around  the 
centre  of  the  ring  on  the  outside,  and  allowing  two  metallic 
springs  ;]/  and  M'  to  press  against  the  denuded  portion  of  the 
coil  as  the  ring  revolves,  and  connecting  these  springs  with 
each  other  by  means  of  a  wire. 

In  the  actual  construction  of  the  Gramme  machine,  the  iron 
ring  is  composed  of  iron  wire,  and  the  copper  coil  around  it  is 
Fig.  4,5.  wound  in  sections,  as  shown  in  Fig- 

ure4i5-  R R are  insulated  metallic 
radial  pieces.  The  ends  of  the 
wires  of  the  sectional  coils  are  con- 
nected with  these  radial  pieces  in 
such  a  way  that  the  coils  are  made 
to  constitute  a  continuous  and  end- 
less conductor,  as  in  Figure  414  ; 
that  is  to  say,  the  end  of  one  coil 
and  the  beginning  of  the  next  are 
connected  to  each  radial  piece.  The  smaller  extensions  of 
the  radial  pieces,  seen  at  the  right,  form  what  is  called  the  com- 
mutator cylinder. 

Figure  416  shows  one  form  of  the  Gramme  machine.  The 
poles  A^and  6"  of  the  permanent  magnet  are  hollowed  out  so  as 
nearly  to  enclose  the  ring.  Metallic  brushes  at  B  press  against 
the  opposite  sides  of  the  commutator  cylinder,  so  as  to  take  off 
the  electricity  from  the  ring  at  points  corresponding  to  M  and 
M'.  This  machine  is  turned  by  hand  by  means  of  the  crank. 
Figure  417  shows  a  Gramme  machine,  designed  to  be  driven  by 
steam  or  water  power,  in  which  the  steel  magnet  is  replaced  by 
a  compound  electro-magnet. 

460.  The  Siemens  Machine.  —  In  the  Siemens  machine  the 
ring  of  the  Gramme  machine  is  replaced  by  a  cylindrical  armature 
composed  of  an  iron  core  on  which  the  coil  of  copper  wire  is 


NATURAL   PHILOSOPHY.  381 

wound  longitudinally.     One  form  of  this  machine  is  shown  in 
Figure  418.     The  compound  electro-magnet  is  made  wide  and 

Fig.  416. 


flat,  so  as  to  give  greater  length  to  the  armature.     The  curved 
portions  above  and  below  the  cylindrical  armature  are  pieces  of 
soft  iron,  which  constitute  the  poles  of  the  compound  electro- 
Fig.  417- 


magnet,  shaped  so  as  nearly  to  enclose  the  armature.     The  wire 
on  the  cylinder  is  wound  in  sections,  as  in  the  Gramme  machine, 


NATURAL    PHILOSOPHY. 
Fig.  418. 


Fig.  419. 


and  the  ends  of  these  sectional 
coils  are  connected  with  insu- 
lated metallic  strips  on  the 
commutator  cylinder,  so  as  to 
form  a  continuous  endless  con- 
ductor, as  in  the  Gramme  ma- 
chine. The  electricity  is  taken 
off  from  these  strips  by  means 
of  metallic  brushes.  The  coils 
of  the  electro-magnet  are  placed 
in  the  circuit,  so  that  the  cur- 
rent developed  by  the  machine 
traverses  them  and  develops 
magnetism.  When  the  machine 
is  started,  the  current,  feeble 
at  first,  is  developed  by  means 
of  the  residual  magnetism  of 
the  electro-magnet.  This  fee- 
ble current  increases  the  mag- 
netism of  the  magnets,  and 
causes  a  stronger  current  to 
be  developed,  and  so  on,  till 
the  current  and  magnetism  at- 
tain their  maximum  strength. 


NATURAL    PHILOSOPHY. 


383 


In  the  Gramme  machine  the  current  is  produced  chiefly 
by  the  change  of  magnetism  ;  and  in  the  Siemens  machine, 
chiefly  by  the  movement  of  the  wire  across  the  magnetic  field. 

461.  The  Edison  Machine.  — The  Edison  machine  is  a  modi- 
fication of  the  Gramme  and  Siemens  machine.  It  is  shown  in 
Figure  419.  The  armature  of  this  machine,  which  is  shown  in 
section  and  in  perspective  in  Figures  420  and  421,  consists  of 
a  core  of  hard  wood,  upon  which  is  wound  transversely  a  coil 
of  iron  wire,  like  thread  on  a  spool.  Upon  this  is  wound 

Fig.  420.  Fig.  421. 


longitudinally  the  coil  of  copper  wire  in  sections.  These  sec- 
tions are  connected  with  insulated  metallic  plates  on  the  com- 
mutator cylinder,  so  as  to  form  a  continuous  endless  conductor. 
The  electricity  is  taken  off  from  the  commutator  by  means  of 
metallic  brushes. 

The  iron  wire  takes  the  place  of  the  ring  in  the  Gramme 
machine.  The  Edison  armature  is  really  the  Gramme  ring  and 
the  Siemens  armature  combined. 

E.   TELEGRAPHY. 

/.    THE    MORSE    SYSTEM. 

462.    The  Principal  Instruments  of  the  Simple  Morse  Tele- 


384  NATURAL    PHILOSOPHY. 

graph. — The  principal  instruments  of  the  simple  Morse 
telegraph  are  the  key,  the'  relay,  and  the  sounder. 

463.    The  Key.  —  The   key    is    used    for   opening   and 
closing  the  circuit.     It  is  shown  in  Figure  422.     Its  essen- 
tial parts  are  shown  in  outline  in  Figure  423.     K  is  the 
lever  ;  a  is  the  axis  on  which  it  turns  ; 
b  is  a  platinum  point  connected  with 
f      K  ^  the  lever ;  c  is  a  stationary  platinum 

^~   "Cf*  point   directly    under    b,    called    the 

Ej*  anvil ;  and  d  is  a  vulcanite  button  by 

which  the  lever  is  pressed  down.  There  is  a  spring  under 
the  lever  of  the  key  which  keeps  it  up  so  as  to  separate  the 
platinum  points  when  the  lever  is  not  pressed  down. 

In  Figure  424  the  key  is  shown  in  the  circuit  of  a  bat- 
Fig  424  tery.     One   pole    of    the 

battery  is  connected  with 
the  anvil  by  a  wire,  and 
the  other  with  the  lever 
at  the  axis.  When  the 
lever  is  up,  the  circuit  is 
B  opened  at  a  by  the  sepa- 

ration of  the  platinum  points,  and  the  current  is  stopped. 

Fig.  425- 


NATURAL    PHILOSOPHY.  385 

When  the  lever  is  pressed  down,  the  circuit  is  closed  by 
the  contact  of  the  platinum  points  at  a,  and  the  current 
starts. 

464.    The  Sounder.  —  The  sounder  is  shown  in   Figure 
425.    Its  essential  parts  are  shown  in  outline  in  Figure  426. 
Fig.  426.  A  is  an  electro-magnet  ;    L  is  a 

lever  ;  b  is  the  axis  on  which  the 
b        S          £  lever  turns  ;  c  is  a  spring  which 

pulls  the  lever  up  ;  e  is  a  piece 
of  soft  iron,  fastened  across  the 
lever  just   over  the  electro-mag- 
net ;  and  d  is  a   piece   of  metal 
against  which  the  lever  strikes  when  it  is  drawn  down. 
Figure  427  shows  the  sounder  and  key  in  circuit.     One 

Fig.  427. 


j=T 
I  —  I 


pole  of  the  battery  is  connected  by  a  wire  with  the  anvil 
of  the  key ;  the  other  pole  is  connected  with  one  end  of 
the  wire  of  the  electro-magnet  of  the  sounder,  and  the  other 
end  of  the  wire  of  this  magnet  is  connected  with  the  lever 
of  the  key  at  the  axis.  These  connections  are  all  made 
by  means  of  binding-screws  on  the  bases  of  the  instru- 
ments. 

When  the  lever  of  the  key  is  up,  the  circuit  is  broken  at 
0,  the  current  is  stopped,  the  electro-magnet  of  the  sounder 
is  inactive,  and  the  lever  of  the  sounder  is  thrown  up  by 
the  spring.  If  we  push  the  lever  of  the  key  down,  con- 
tact is  made  at  tf,  which  closes  the  circuit ;  the  current 
starts,  the  electro-magnet  of  the  sounder  becomes  active, 
and  the  lever  of  the  sounder  is  drawn  down  by  the  pull  of 


386 


NATURAL   PHILOSOPHY. 


the  magnet  upon  the  iron  above  it.'  As  the  lever  is  drawn 
down,  it  clicks  because  of  its  striking  the  metallic  stop  at 
the  end. 

The  clicking  of  the  sounder  is  controlled  by  the  key, 
even  when  these  are  miles  apart,  for  the  sounder  clicks 
every  time  the  lever  of  the  key  is  depressed.  Letters  and 
words  are  indicated  by  combinations  of  long  and  short 
intervals  between  the  clicks.  The  operator  listens  to  the 
sounder  just  as  we  listen  to  one  who  is  talking  to  us,  and 
soon  becomes  able  to  follow  it  as  readily. 

465.  The  Register.  —  Sometimes  an  instrument  called 
the  register  is  used  for  receiving  the  message  instead  of  the 
sounder.  The  essential  parts  of  this  instrument  are  shown 
in  Figure  428.  It  resembles  the  sounder  in  construction 

Fig.  428. 


and  action.  At  the  back  end  of  the  lever  there  is  a  point 
B,  and  just  above  this  point  a  strip  of  paper  C  is  carried 
along  by  clockwork  between  two  rollers  at  D.  When  the 
lever  is  drawn" to  the  magnet,  the  point  is  "thrown  against 
the  paper  and  scratches  a  line  on  it.  This  line  will  be  long 
or  short  according  to  the  time  the  lever  is  held  down. 
The  long  lines  are  called  dashes  and  the  short  lines  dots. 
These  dots  and  dashes  correspond  to  the  short  and  long 
intervals  between  the  clicks  of  the  sounder,  and  their  com- 
binations form  the  letters  of  the  alphabet. 

466.    The  Relay.  —  On  long  lines,  in  which  there  are  a 
number  of  stations,  the  current  from  the  main   battery  is 


NATURAL    PHILOSOPHY. 


387 


not  strong  enough  to  work  the  sounders  with  sufficient 
force.  This  necessitates  the  use  of  an  instrument  called 
the  relay.  This  instrument  is  shown  in  Figure  429,  and 

Fig.  429. 


the  essential  parts  of  it  are  shown  in  outline  in  Figure  430. 
A  is  an  electro-magnet ;  /  is  the  lever,  which  turns  upon 
an  axis  at  b ;  c  is  a  piece  of  soft  iron 
fastened  across  the  lever  in  front  of  the 
electro-magnet ;  /is  a  spring  for  pulling 
the  lever  back  ;  d  and  e  are  two  platinum 
points,  the  former  fastened  to  the  lever 
and  the  latter  stationary, 

Figure  431   shows  the  way  in  which  the  key,  relay,  and 
sounder  are  connected.    The  full  line  represents  the  circuit 

Fig.  431- 

~~~\ 


of  the  main  battery  M ;  and  the  dotted  line,  of  the  local 
battery  Z.  '  One  pole  of  the  main  battery  is  connected  with 


388  NATURAL    PHILOSOPHY. 

the  anvil  of  the  key,  and  the  other  with  one  end  of  the  wire 
of  the  electro-magnet  of  the  relay.  The  other  end  of  the 
wire  of  this  magnet  is  connected  with  the  lever  of  the  key 
at  the  axis.  One  pole  of  the  local  battery  is  connected  to 
the  lever  of  the  relay,  and  the  other  pole  to  the  electro- 
magnet of  the  sounder  and  then  to  the  stationary  platinum 
point  of  the  relay.  When  the  lever  of  the  key  is  up,  the 
main  circuit  is  opened  at  a,  the  current  is  stopped,  the 
electro-magnet  of  the  relay  is  inactive,  the  lever  of  the 
relay  is  drawn  back  by  the  spring,  the  local  circuit  is 
opened  at  b  by  the  separation  of  the  platinum  points,  the 
electro-magnet  of  the  sounder  is  inactive,  and  the  bar  of 
the  sounder  is  thrown  up  by  the  spring.  On  pushing  down 
the  lever  of  the  key,  contact  is  made  at  a,  the  main  circuit 
is  closed,  the  electro-magnet  of  the  relay  becomes  active, 
the  lever  of  the  relay  is  drawn  forward,  contact  is  made  at 
6,  the  local  circuit  is  closed,  the  electro-magnet  of  the 
sounder  becomes  active,  and  the  lever  of  the  sounder  is 
drawn  down.  Thus  the  levers  of  the  relay  and  sounder 
vibrate  in  unison,  but  each  is  worked  by  a  different  battery. 
The  vibration  of  the  lever  of  the  relay  is  controlled  by  the 
key,  and  controls  the  vibration  of  the  lever  of  the  sounder 
by  opening  and  closing  the  local  circuit. 

467.  The  two  Terminal  Stations  of  a  Line.  —  Figure  432 
shows  the  arrangement"  of  the  instruments  and  circuits  for 
two  terminal  stations.  For  convenience,  half  of  the  main 
battery  is  placed  at  each  station.  There  is  also  a  key,  a 
relay,  and  a  sounder  at  each  station.  One  pole  of  the 
main  battery,  say  the  negative,  at  New  York  is  connected 
to  the  earth  by  a  wire  running  to  a  large  copper  plate  £ 
sunk  in  the  ground.  A  wire  runs  from  the  positive  pole  of 
the  battery  to  the  anvil  of  the  key  K,  then  from  the  lever 
of  the  key  to  the  electro-magnet  of  the  relay  A',  then  from 
the  relay  to  the  line  and  along  the  line  to  Boston,  then  to 
the  electro-magnet  of  the  relay  R1,  then  to  the  lever  Of  the 


D- 


NATURAL    PHILOSOPHY.  389 


• 


3QO  NATURAL    PHILOSOPHY. 

key  K',  then  from  the  anvil  of  the  key  to  the  negative  pole 
of  this  part  of  the  main  battery,  and  from  the  positive  pole 
of  the  battery  to  the  copper  plate  E'  in  the  earth.  The 
circuit  is  completed  by  the  earth,  the  electricity  passing 
one  way  over  the  line  and  back  through  the  earth.  Each 
local  battery  is  connected  with  its  relay  and  sounder  as  in 
the  previous  section. 

When  the  line  is  not  in  operation,  the  main  circuit  is 
closed  at  each  key  by  pulling  the  side  lever  seen  in  Figure 
422  up  against  the  anvil.  This  connects  the  axis  of  the 
lever  with  the  anvil,  and  closes  the  circuit,  although  the 
levers  of  the  keys  are  up.  The  electro-magnets  of  both 
relays  are  now  active,  the  levers  of  both  relays  are  drawn 
forward,  both  local  circuits  are  closed,  the  electro-magnets 
of  both  sounders  are  active,  and  the  levers  of  both  sounders 
are  drawn  down.  When  the  operator  at  one  of  the  stations 
wishes  to  send  a  message,  he  pulls  back  the  side  lever  of 
his  key.  This  opens  the  main  circuit,  and  causes  all  the 
electro-magnets  to  become  inactive,  and  all  of  the  levers 
to  be  thrown  back.  On  working' his  key,  the  levers  of 
both  relays  and  of  both  sounders  are  made  to  vibrate. 
His  own  sounder  clicks  as  well  as  that  at  Boston.  When 
the  operator  has  finished  his  message,  he  closes  his  key  by 
pulling  the  side  lever  against  the  anvil.  Should  both 
operators  start  at  the  same  instant  to  send  messages,  the 
fact  would  be  revealed  by  the  confusion  of  the  signals 
given  by  each  sounder,  and  one  operator  would  close  his 
key  and  wait  for  the  other  to  finish.  Should  the  operator 
at  the  receiving  station  desire  to  interrupt  the  one  sending 
the  message  to  ask  him  to  repeat,  or  for  any  other  purpose, 
he  has  merely  to  open  his  key  so  as  to  break  the  current. 

468.  A  Way  Station.  —  One  of  the  simplest  methods  of 
introducing  the  instrument  of  a  way  station  into  the  circuit 
is  shown  in  Figure  433.  A  and  B  are  two  brass  buttons 
turning  on  pivots  at  the  top.  Under  the  bottom  of  each 


NATURAL    PHILOSOPHY 


D- 


392  NATURAL    PHILOSOPHY. 

button,  as  it  stands  in  the  diagram,  is  a  metallic  disc  D,  E. 
A  wire  runs  from  one  of  the  metallic  discs  to  the  electro- 
magnet of  the  key  K1  and  thence  to  the  anvil  of  the  key 
K1.  A  wire  runs  from  the  other  disc  to  the  lever  of  the  key. 
There  is  a  third  metallic  disc  at  C  between  the  buttons. 
When  the  buttons  are  on  the  discs  D  and  E,  the  key  and 
the  electro-magnet  of  the  relay  are  in  the  main  circuit. 
The  sounder  and  local  circuit  are  arranged  precisely  as  in 
the  terminal  stations.  When  not  in  operation,  the  key  is 
kept  closed  by  means  of  the  side  lever. 

It  will  be  seen  at  once  that  the  levers  of  the  relay  and 
sounder  will  vibrate  when  the  key  at  either  terminal  station 
is  worked,  and  also  that  the  levers  of  the  relays  and 
sounders  at  the  terminal  stations  will  vibrate  on  working 
the  key  at  the  way  station.  When  the  buttons  A  and  B 
are  both  turned  upon  the  disc  C,  the  instrument  of  the  way 
station  will  be  cut  out  of  the  circuit,  which  will  be  completed 
through  the  buttons,  these  being  now  in  contact  with  each 
other. 

When  any  key  at  any  station  is  worked,  the  sounders  of 
every  station  which  is  not  cut  out  will  click.  The  name 
of  the  station  for  which  the  message  is  designed  is  first 
called,  and  only  the  operator  at  that  station  attends  to  the 
message. 

There  are  means  at  each  way  station  to  connect  one  of 
the  wires  with  the  ground  and  the  other  wire  with  the  line 
on  either  side,  so  that  the  operator  may  use  that  side  alone, 
in  case  the  line  is  injured  in  any  way  on  the  other  side  of 
his  station.  The  chief  reason  that  the  main  battery  is 
divided  between  the  terminal  stations  is  to  enable  a  way 
station  to  use  the  line  on  either  side  in  case  of  necessity. 

II.   DUPLEX  TELEGRAPHY. 

469.  Two  Obstacles  to  be  overcome  in  Duplex  Telegraphy.  — 
By  duplex  telegraphy  is  meant  a  system  of  telegraphy  in  which 


NATURAL    PHILOSOPHY. 


393 


messages  are  sent  both  ways  over  the  same  wire  at  the  same 
time.  There  must  be  a  battery  at  each  of  the  stations  between 
which  the  messages  are  sent.  In  the  simple  Morse  system,  as 
we  have  seen,  the  relay  and  sounder  respond  to  the  message  at 
the  station  from  which  it  is  sent  as  well  as  at  that  to  which  it  is 
sent.  The  chief  obstacle  to  be  overcome  in  duplex  telegraphy 
is  to  keep  the  relay  and  sounder  from  responding  to  the  message 
at  the  station  from  which  it  is  sent,  so  that  they  shall  respond 
only  at  the  station  to  which  the  message  is  sent.  The  second 
difficulty  is  to  prevent  the  opening  of  the  key  at  one  station 
from  opening  the  circuit  of  the  battery  at  the  other  station. 

Fig.  434- 
line 


JS  — 


I 


470.  The  Duplex  Transmitter.  —  The  second  of  these  diffi- 
culties is  met  by  the  use  of  what  is  called  the  duplex:  transmitter. 
The  essential  parts  of  this  instrument  and  the  way  in  which  it  is 
connected  with  the  batteries  and  with  the  ground  are  shown  in 
Figure  434.  Tis  an  electro-magnet;  L  is  a  lever  turning  on  an 
axis  at  G;  c  is  an  insulating  support  for  the  spring  d ;  a  is  a 
fixed  platinum  point  above  the  spring;  b  is  a  second  platinum 
point  attached  to  the  hooked  end  of  the  lever  :  and /"is  a  spring 
coil  for  throwing  the  lever  up.  A  bar  of  soft  iron  is  fastened 
to  the  lever  over  the  electro-magnet.  The  key  and  the  electro- 
magnet of  the  transmitter  are  in  the  circuit  of  a  little  local 
battery,  as  shown  by  the  dotted  lines.  The  -|-  pole  of  the  dis- 
tant battery  M'  is  connected  with  the  spring  on  the  insulating 
support.  The  -\-  pole  of  the  battery  M  is  connected  with  the 


394  NATURAL   PHILOSOPHY. 

lever  at  G.     The  stationary  platinum  point,  and  the  negative 
poles  of  both  batteries  are  connected  with  the  ground. 

When  the  key  is  open,  the  electro-magnet  of  the  transmitter 
is  inactive,  and  the  lever  of  the  transmitter  is  thrown  up.  The 
platinum  point  b  is  in  contact  with  the  spring,  and  the  point  a  is 
separated  from  it.  The  circuit  of  the  distant  battery  is  now 
closed  by  way  of  the  spring  d,  the  platinum  point  £,  the  lever 
and  the  battery  M.  The  circuit  of  the  battery  M  is  closed  by 
the  contact  of  b  with  the  spring  d, 

When  the  key  is  closed,  the  electro-magnet  of  the  transmitter 
is  active,  and  the  lever  is  drawn  down.  As  the  magnet  end  of 
the  lever  moves  down,  the  hooked  end  moves  up.  The  spring  d 
also  moves  up  till  it  is  stopped  by  the  platinum  point  a.  The 
point  b  is  carried  up  a  little  higher,  and  is  separated  from  the 
spring,  a  is  now  in  contact  with  the  spring,  and  b  is  separated 
from  it  (Figure  434).  The  circuit  of  the  distant  battery  is  now 
closed  by  way  of  the  spring  d,  the  platinum  point  a,  and  the 
ground  wire  connected  with  it,  and  the  circuit  of  the  battery  M 
is  open. 

It  is  thus  seen  that  as  the  key  is  closed  and  opened,  the  plati- 
num points  a  and  b  are  alternately  brought  in  contact  with  the 
spring  d,  and  that  whatever  may  be  the  position  of  the  bar  of 
the  transmitter,  the  circuit  of  the  distant  battery  M'  is  closed, 
while  the  circuit  of  the  battery  M  is  alternately  opened  and 
closed. 

471.  The  Differential  Duplex.— In  the  differential  duplex 
the  relay  is  kept  from  responding  to  the  outgoing  message  by 
making  it  differential.  A  differential  relay  is  one  whose  electro- 
magnet is  wound  with  double  coils,  so  that  two  currents  may  be 
sent  through  these  coils  in  opposite  directions.  When  these 
currents  are  equal  the  relay  is  inactive,  and  when  they  are  un- 
equal the  relay  is  active. 

Figure  435  represents  two  terminal  stations  arranged  for  the 
duplex  system.  The  sounders  are  not  shown,  because  they  are 
connected  with  the  relays  as  in  the  simple  Morse  system,  and 
are  controlled  by  the  vibration  of  the  levers  of  the  relays.  Their 
action  is  the  same  as  before.  For  clearness  the  two  coils  of 
the  differential  relays  are  represented  as  apart  on  the  same  iron 
core.  They  are  usually  wound  one  over  the  other. 


D 


NATURAL   PHILOSOPHY. 
X 


396  NATURAL    PHILOSOPHY. 

The  positive  pole  of  the  battery  M  is  connected  with  the 
stationary  platinum  point  a  of  the  transmitter.  A  wire  runs 
from  the  spring  d  of  the  transmitter  to  the  point  A,  where  it 
divides  into  two  branches  B  and  C.  The  branch  C  traverses 
the  coil/" of  the  relay  magnet,  and  then  passes  directly  to  earth 
through  the  resistance  box  X.  The  branch  B  traverses  the  coil 
e  of  the  relay  magnet  and  then  passes  to  the  line.  The  battery 
M'  at  the  other  station  is  connected  to  the  transmitter  and  relay 
in  exactly  the  same  way.  The  negative  poles  of  both  batteries 
and  the  levers  of  the  transmitters  are  connected  with  the  ground. 
The  resistance  boxes  X  and  X'  are  adjusted  so  that  the  resist- 
ance of  the  branch  C  or  C'  shall  be  equal  to  that  of  the  branch 
B  or  B',  including  the  whole  line. 

When  the  key  K  is  closed  the  electro-magnet  of  the  trans- 
mitter is  made  active,  the  lever  of  the  transmitter  is  drawn 
down,  the  spring  d  is  separated  from  b  and  brought  in  contact 
with  a,  and  the  circuit  of  the  battery  M  is  closed. 

The  current  from  this  battery,  on  reaching  the  point  A,  divides 
into  two  equal  parts  ;  one  of  which  passes  through  the  wire  C, 
the  coil /and  the  resistance  box  X  to  the  earth  and  back  to  the 
negative  pole  of  the  battery;  the  other  passes  through  the  wire 
B,  the  coil  e,  and  the  line  to  the  distant  station.  It  then  passes 
through  the  coil  e',  the  wire  £',  the  spring  d',  and  thence  to 
the  earth,  either  by  the  point  a'  and  the  battery  M',  or  by  the 
point  b',  the  lever  and  the  ground  wire  G',  according  as  a'  or 
b'  is  in  contact  with  the  spring  d'.  As  the  outgoing  current 
divides  equally  at  A,  the  magnet  R  will  remain  inactive  while 
the  portion  which  passes  over  the  line  will  make  R'  active. 
Hence  R'  only  will  respond  to  the  current  sent  from  the  battery 
M.  In  the  same  way  it  may  be  seen  that  R  alone  will  respond 
to  the  current  sent  from  the  battery  M' . 

When  currents  are  sent  from  both  batteries  at  the  same  time, 
if  the  batteries  are  in  opposition,  as  in  the  diagram,  the  currents 
from  the  two  batteries  will  more  or  less  completely  neutralize 
each  other  in  the  line  branch,  BB',  without  neutralizing  each 
other  at  all  in  the  earth  branches,  C  and  C1.  The  currents  will 
therefore  be  unequal  in  the  two  sets  of  coils  at  each  relay,  and 
both  the  electro-magnets  will  be  active.  The  electro-magnet  at 
the  left  will  be  active  just  as  long  as  the  key  at  the  right  is 
closed,  and  vice  versa. 


NATURAL    PHILOSOPHY.  397 

472.  The  Use  of  Condensers  with  the  Duplex.  —  As  has  already 
been  stated,  a  part  of  the  electricity  that  flows  into  a  wire  is 
used  in  charging  it.     Now,  when  contact  is  broken  at  a,  it  is 
found  that  a  portion  of  the  charge  which  the  line  has  received 
from  the  battery  M  rushes  to  earth  through  the  coil  e,  the  spring 
d,  the  point  b,  and  the  ground  wire  G.    This  current  would  make 
the  magnet  A'  active,  and  give  a  false  signal  on  the  sounder  con- 
nected with  this  relay,  were  it  not  balanced  by  an  equal  current 
sent  back  through  the  coil  /.     This  return  current  is  obtained 
by  means  of  the  condenser  F.     This  condenser  is  charged  by 
the  electricity  flowing  through  the  branch  Cto  the  earth.    When 
contact  is  broken  at  a,  the  coatings  of  the  condenser  connected 
with  the  wire  near  the  resistance  box  at  once  discharge  them- 
selves through  the  wire  to  the  earth.     As  the  resistance  is  much 
less  by  way  of  the  coil/",  and  the  spring  </,  and  the  ground  wire 
G,  than  through  the  resistance  box  X,  the  greater  part  of  the 
discharge  takes  this  route.     The  condenser  is  adjusted  so  that 
the  discharge  from  it  through  f  is  just  equal  to  the  discharge 
from  the  line  through  e.    The  condenser  F'  at  the  other  station 
acts  in  a  similar  way. 

473.  The  Bridge  Duplex.  —  Another  way  to  keep  the  relay 
from  responding  to  the  outgoing  current  is  to  place  it  on  a 
bridge.     This  arrangement  is  shown  in  Figure  436.     The  keys, 
transmitters,  and  batteries  are  arranged  exactly  as  in  the  differ- 
ential duplex.     At  A  the  circuit  divides  so  as  to  form  a  bridge, 
the  four  branches  of  which  are  A  B,  the  line,  A  C,  and  C  G  ; 
and  the  bridge  proper  B  C.     The  resistance  boxes  w,  x,  and_y 
are  introduced   into  three  of  these  branches,  and  adjusted  so 
that  the  resistance  of  A  B  is  to  that  of  the  line  as  the  resist- 
ance of  A  C  is  to  that  of  C  G.     The  relay  R  is  introduced  into 
the  bridge  B  C.     This  is  an  ordinary  relay.     The  arrangement 
at  A'  is  in  all  respects  similar  to  that  at  A. 

The  outgoing  current  from  the  battery  M  divides  at  A  into 
two  portions,  one  of  which  passes  through  A  C  and  C  G  to  the 
earth,  and  the  other  through  A  B  and  the  line  to  the  distant 
station.  None  of  the  outgoing  current  crosses  the  bridge  B  C, 
and  hence  the  relay  R  does  not  respond  to  this  current.  As  the 
portion  of  the  current  which  has  traversed  the  line  crosses  to 
B1  it  again  divides,  a  part  of  it  going  through  B'C'  to  the  earth, 


398 


NATURAL   PHILOSOPHY. 


NATURAL   PHILOSOPHY.  399 

and  another  part  of  it  through  B'  A'  and  the  transmitter  to  the 
earth.  The  first  portion  works  the  relay  R'.  In  a  similar  way, 
none  of  the  current  sent  back  from  the  battery  M'  will  pass 
through  the  wire  B'  C'  so  as  to  work  the  relay  R',  while  a  por- 
tion of  it  will  cross  B  C  and  work  the  relay  R.  Thus,  R  and 
the  sounder  connected  with  it  will  deliver  only  the  message  sent 
by  key  K',  and  R'  and  the  sounder  connected  with  it,  only  the 
message  sent  by  key  K. 

The  condensers  F  and  F'  are  used  to  send  back  through 
C  B  and  C'  B'  discharges  to  neutralize  those  sent  from  the  line 
through  the  wire  on  breaking  contact  at  a  and  a'. 

III.   QUADRUPLEX    TELEGRAPHY. 

474.  The  Principle  of  the  Quadruple*.  —  By   quadruple* 
telegraphy  is  meant  a  system  of  telegraphy  in  which  four  mes- 
sages may  be  sent  over  the  same  wire  at  the  same  time,  —  two 
in  each  direction.      To  send  two  messages  the  same  way  at  the 
same  time,  it  is  necessary  to  have  one  relay  worked  by  changing 
the  direction  of  the  current,  and  one  by  changing  the  strength 
of  the  current ;  also  to  have  a  transmitter  controlled  by  one  key 
arranged  so  as  to  change  the  direction  of  the  current,  and  a 
transmitter  controlled  by  the  other  key  arranged  so  as  to  change 
the  strength  of  the  current. 

475.  The  Polarized  Relay.  —  The  polarized  relay  differs  from 
an  ordinary  neutral  relay  simply  in  having  a  small  steel  magnet 
on  the  lever  in  place  of  the  bar  of  soft  iron.     There  is  usually 
no  spring  acting  on  the  lever.     When  the  current  passes  through 
the  coils  of  the  electro-magnet  in  one  direction,  the  poles  of  the 
electro-magnet  are  unlike  those  of  the  permanent.    There  is  then 
attraction,  and  the  lever  is  drawn  forward.     On  reversing  the 
direction  of  the  current  the  poles  of  the  electro-magnet  are  re- 
versed, and  become  like  those  of  the  steel  magnet  in  front  of  them. 
There  is  now  repulsion,  and  the  lever  of  the  relay  is  thrown  back. 

476.  The  Pole-Changer.  —  The  transmitter  used  for  changing 
the  direction  of  the  current  is  called  the  pole-changer.      The 
essential  parts  of  this  instrument  and  its  connection  with  the  key 
and  a  battery  are  shown  in  Figure  437.     The  pole-changer  is 
connected  with  the  key  in  precisely  the  same  way  as  the  duplex 
transmitter.      At  the  end  of  the  lever  away  from  the  electro- 


400 


NATURAL    PHILOSOPHY. 


magnet  are  two  springs,  a  and  b.  On  each  of  these  springs  are  two 
platinum  points  (c,  d,  and  e,  /).  Between  the  springs  is  a  back- 
stop^, having  two  platinum  points,  h  and  /,  upon  it,  facing  the 
points  c  and  e.  The  end  of  the  lever  has  also  two  platinum 
points,  k  and  /,  upon  it,  facing  the  points  </and/". 

The  back-stop^  is  connected  with  the  line,  the  spring  a  with 
the  negative  pole  of  the  battery,  the  spring  b  with  the  positive 
pole  of  the  battery,  and  the  lever  with  the  ground. 

When  the  key  is  closed,  the  electro-magnet  of  the  pole- 
changer  is  active,  the  lever  is  drawn  to  the  magnet,  and  the 
other  end  of  the  lever  is  raised,  and  contact  is  made  between 
d  and  k  and  between  e  and  i,  and  broken  between  c  and  h  and 


between  /and/  The  positive  pole  of  the  battery  is  now  con- 
nected with  the  line  through  the  points  e  and  z,  and  the  negative 
pole  with  the  earth  through  the  points  d  and  k.  When  the  key 
is  open,  the  electro-magnet  of  the  pole-changer  is  inactive,  and 
the  magnet  end  of  the  lever  is  thrown  up,  and  the  other  end  of 
the  lever  thrust  down.  Contact  is  thus  broken  between  ^/and  k 
and  between  e  and  z,  and  made  between  /  and  /  and  between 
c  and  h.  The  negative  pole  of  the  battery  is  now  connected 
with  the  line  through  the  points  c  and  ^,  and  the  positive  pole 
with  the  earth  through  the  points/and  /  (Figure  437).  As  the 
pole-changer  end  of  the  lever  rises,  the  spring  b  follows  it  until 
it  is  stopped  by  the  platinum  point  /  on  the  back-stop  g.  At  this 
instant  the  point  k  strikes  the  point  d.  The  lever  then  raises 


NATURAL    PHILOSOPHY. 


401 


the  spring  a,  and  so  breaks  contact  between  c  and  h.  At  the 
same  time  it  leaves  the  spring  b  behind,  and  so  breaks  contact 
between /and  /.  The  reverse  takes  place  when  this  end  of  the 

lever  is  lowered. 

Fig.  438. 


477.    Simultaneous    Transmission   of  two  Messages  in   the 
Same  Direction  on  a  IVire.  —  The  arrangement  of  the  instru- 


402  NATURAL    PHILOSOPHY. 

ment  at  a  terminal  station  for  the  simultaneous  transmission  of 
two  messages  in  the  same  direction  is  shown  in  Figure  438. 
T  is  a  duplex  transmitter,  employed  for  changing  the  strength 
of  the  current.  It  is  worked  by  the  local  battery  B  and  the 
key  K.  T'  is  a  pole-changer,  used  for  changing  the  direction 
of  the  current.  It  is  worked  by  the  local  battery  B'  and  the 
key  K '.  R  is  an  ordinary  neutral  relay,  and  S  is  its  sounder. 
R'  is  an  ordinary  polarized  relay,  and  S'  is  its  sounder.  These 
sounders  are  worked  by  the  local  batteries  L  B  and  L  B'. 

M  is  the  main  battery.  The  positive  pole  of  this  battery  is 
connected  with  the  platinum  point  a  of  the  duplex  transmitter, 
and  the  negative  pole  with  the  spring  a  of  the  pole-changer. 
The  spring  d  oi  the  transmitter  is  connected  with  the  spring  b 
of  the  pole-changer.  The  back-stop  g  of  the  pole-changer  is 
connected  with  the  line  through  the  electro-magnet  of  the  relays 
R'  and  R.  The  lever  of  the  transmitter  is  connected  with  the 
positive  plate  P  of  the  main  battery,  and  the  lever  of  the  pole- 
changer  is  connected  with  the  ground.  At  the  other  terminal 
station  there  will  be  precisely  the  same  instruments,  arranged 
in  precisely  the  same  way. 

When  the  key  K  is  open,  the  electro-magnet  of  the  transmit- 
ter is  inactive,  the  magnet  of  the  lever  is  thrown  up,  and  the 
hooked  end  is  thrust  down.  The  platinum  point  b  is  in  contact 
with  the  spring  d,  and  the  point  a  is  separated  from  it.  The 
positive  plate  P  of  the  main  battery,  or  the  positive  pole  of  %  of 
the  battery,  is  now  connected  with  the  spring  b  of  the  pole- 
changer  through  the  point  b  of  the  transmitter.  The  remaining 
^  of  the  battery  are  cut  out  of  the  circuit,  since  the  point  a  is 
separated  from  the  spring  d  of  the  transmitter. 

When  key  K  is  closed,  the  electro-magnet  of  the  transmit- 
ter is  active,  and  the  magnet  end  of  the  lever  is  drawn  down, 
and  the  other  end  is  thrust  up.  The  platinum  point  a  is  now 
brought  into  contact  with  the  spring  </,  and  b  is  separated  from 
it.  The  positive  pole  of  the  whole  battery  is  now  connected  with 
the  spring  b  of  the  pole-changer  through  the  point  a  of  the 
transmitter. 

The  effect  of  closing  key  K  is  to  put  the  whole  battery  in 
circuit ;  and  of  opening  it,  to  cut  out  a  part  of  the  battery  from 
the  circuit. 


NATURAL    PHILOSOPHY.  403 

When  key  K'  is  open,  the  magnet  of  the  pole-changer  is  in- 
active, the  magnet  end  of  the  lever  is  up,  and  the  other  end 
down.  The  positive  pole  is  now  connected  with  the  ground 
through  the  spring  b,  the  points  f  and  /,  the  lever,  and  the 
wire  Gj  and  the  negative  pole  is  connected  with  the  line  through 
the  spring  a,  the  points  c  and  h,  and  the  back-stop  g. 

When  K'  is  closed,  the  electro-magnet  of  the  pole-changer  is 
active,  the  magnet  end  of  the  lever  is  pulled  down,  and  the  other 
end  is  thrust  up.  The  positive  pole  will  now  be  connected  with 
the  line  through  the  spring  i>,  points  e  and  z,  and  the  back-stop  g ; 
and  the  negative  pole  is  connected  with  the  ground  through  the 
spring  a,  the  points  d  and  k,  the  lever,  and  the  wire  G. 

The  effect  of  closing  K'  is  to  put  the  positive  pole  of  the 
battery  to  the  line,  and  the  negative  pole  to  the  earth ;  and  of 
opening  it,  to  put  the  negative  pole  to  the  line,  and  the  positive 
pole  to  the  earth.  In  other  words,  closing  K'  reverses  the 
direction  of  the  current. 

The  neutral  relay  R  is  so  adjusted  that  it  requires  the  cur- 
rent from  the  whole  battery  to  overcome  the  tension  of  the 
spring/",  so  as  to  pull  the  lever  forward  and  break  contact  be- 
tween the  platinum  points  at  m.  The  action  of  this  relay  is  inde- 
pendent of  the  direction  of  the  current.  The  local  circuit  of  the 
sounder  *S"  will  therefore  be  closed  when  key  K  is  open,  and 
opened  when  key  K  is  closed  ;  that  is  to  say,  the  sounder  ^ 
delivers  the  message  sent  by  key  K,  and  that  message  only. 

The  polarized  relay  ^ '  is  so  arranged  that  it  can  be  worked 
by  the  smaller  portion  of  the  battery  as  well  as  by  the  whole  bat- 
tery, and  so  that  like  poles  on  the  electro-magnet  and  on  the 
steel  magnet  are  together  when  the  key  K1  is  open.  In  this 
case  the  lever  is  repelled,  and  contact  made  at  «,  and  the  level 
circuit  of  sounder  S'  is  closed.  On  closing  key  K',  the  line 
current  and  the  poles  of  the  electro- magnet  R'  are  reversed. 
The  steel  magnet  is  now  attracted,  the  lever  drawn  forward, 
and  contact  broken  at  n.  This  opens  the  local  circuit  of  the 
sounder  S'.  As  the  relay  R'  is  worked  only  by  changing  the 
direction  of  the  current,  it  responds  only  to  the  action  of  key  A''. 
As  this  relay  can  be  worked  by  a  part  of  the  battery  as  well  as 
by  the  whole,  R '  will  respond  to  the  working  of  K'  whether  K  is 
open  or  closed. 


404  NATURAL   PHILOSOPHY. 

Of  course,  the  instruments  at  the  distant  station  would  re- 
spond in  the  same  way  as  these  in  this  station,  as  they  are  in  the 
same  circuits.  Thus,  two  messages  may  be  sent  out  at  the  same 
time, — one  by  each  of  the  keys, — and  each  will  be  delivered 
by  the  corresponding  sounder  without  any  confusion.  Of  course, 
the  two  sounders  are  placed  so  far  apart  that  the  operator  who 
is  attending  to  one  is  not  confused  by  the  clicking  of  the 
other. 

478.  The  Quadruplex  System.  —  By  using  differential  relays, 
or  by  placing  the  relays  on  a  bridge,  the  sounders  would  be  kept 
from  responding  to  the  outgoing  message,  and  would  at  the  same 
time  be  in  readiness  to  deliver  incoming  messages,  as  in   the 
duplex  system  ;  that  is,  by  duplexing  the  arrangement  just  de- 
scribed, four  messages   may  be  sent  simultaneously   over   the 
same  wire,  —  two  in  each  direction.     The  differential  method  of 
duplexing  is  the  one  ordinarily  used  in  the  quadruplex  system. 

The  use  of  the  duplex  and  quadruplex  system  is  rapidly  ex- 
tending. The  Western  Union  Company  already  use  the  quadru- 
plex system  on  200  lines.  The  tendency  of  these  two  systems 
is  to  drive  the  simple  Morse  system  entirely  from  the  field, 
except  on  lines  where  there  is  very  little  business. 
\ 

IV.   SUBMARINE    TELEGRAPHY. 

479.  The  Cable.  —  In  submarine  telegraphy,  the  conducting 
wire,  instead  of  being  insulated  on  poles  by  means  of  glass  insu- 
lators, is  insulated  by  being  enclosed  in  an  insulating  sheath.   The 
insulator  used  should  be  sufficiently  tough  not  to  break  in  the 
operation  of  laying  the  cable,  and  it  should  at  the  same  time  have 
as  low  a  specific  inductive  capacity  as  possible.    The  conductor  is 
a  strand  of  rather  fine  copper  wire.     The  insulating  sheath  is  of 
gutta-percha.  This  is  protected  by  a  layer  of  tarred  hemp,  and  the 
whole  is  surrounded  by  iron  wire  for  greater  strength.     The  iron 
wire  is  usually  protected  by  an  outer  coating  of  some  kind.     It  is 
necessary  that  the  conducting  wire  should  be  very  carefully  insu- 
lated ;  and  it  is  desirable  to  have  the  specific  inductive  capacity 
of  the  insulator  as  low  as  possible. 

480.  Duration  of  the  Variable  State  in  a  Cable.  —  While  a 
wire  is  becoming  statically  charged  or  discharged,  the  current 
at  the  distant  end  of  the  wire  is  in  a  variable  state.     When  the 


NATURAL    PHILOSOPHY.  405 

wire  is  becoming  charged,  the  current  at  the  distant  end  is 
feeble  at  first,  and  rises  gradually  to  its  maximum  strength. 
It  then  remains  of  constant  strength  till  the  current  at  the  other 
end  is  stopped  and  the  wire  begins  to  discharge  itself.  It  then 
gradually  dies  away.  The  duration  of  this  variable  state  in- 
creases with  the  capacity  of  the  conducting  wire.  On  land  lines 
it  is  exceedingly  short,  but  in  a  long  submarine  cable,  owing  to 
its  very  much  greater  capacity,  the  variable  state  lasts  several 
seconds.  When  a  signal  is  sent  from  Valentia,  it  is  about  two 
tenths  of  a  second  before  it  begins  to  be  felt  at  Newfoundland, 
and  it  is  three  seconds  before  the  current  reaches  its  maximum 
strength  ;  and  if  the  cable  were  left  to  discharge  itself  in  its  own 
way,  the  current  would  be  equally  long  in  stopping. 

481.  The  Transmitting  Key.  —  Owing  to  the  feebleness  of 
the  current  which  first  reaches  the  distant  end  of  the  cable,  in 
order  that  the  signals  may  be  received  promptly,  it  is  necessary 
to  use  a  very  sensitive  receiving  instrument ;  and  owing  to  the 
duration  of  the  variable  state  on  starting  or  stopping  the  current, 
in  order  that  the  signals  may  follow  each  other  rapidly,  it  is  neces- 
sary to  provide  some  means  for  promptly  discharging  the  cable. 

The  transmitting  key  is  shown  in  Figure  439.     E  and  L  are 
two  levers  connected  respectively  with  the  earth  F;g  439 

and  the  line.  When  not  depressed,  both  of 
these  levers  rest  against  the  upper  bar  C,  which 
is  connected  with  the  positive  pole  of  the  bat- 
tery. When  either  is  depressed,  it  is  separated 
from  the  upper  bar  and  is  brought  into  contact 
with  the  lower  bar  Z,  which  is  connected  with 
the  negative  pole  of  the  battery.  On  depressing 
E,  the  positive  pole  of  the  battery  is  connected 
with  the  cable  and  the  negative  pole  with  the 
earth.  On  releasing  E  and  depressing  L,  the 
negative  pole  of  the  battery  is  connected  with  the  cable  and 
the  positive  pole  with  the  earth.  By  depressing  the  levers  alter- 
nately, the  direction  of  the  current  in  the  cable  is  reversed. 

482.  The  Receiving  Instrument.  —  Thomson's  reflecting  gal- 
vanometer is  one  of  the  receiving  instruments  employed  on  long 
submarine  cables.     As  the  direction  of  the  current  in  the  cable 
is  reversed,  the  spot  of  light,  reflected  from  the  mirror,  moves 


4o6 


NATURAL    PHILOSOPHY. 


towards  the  right  or  towards  the  left  as  the  case  may  be.  The 
letters  are  indicated  by  combinations  of  these  movements,  as  by 
the  combinations  of  the  long  and  short  intervals  in  the  case  of 
the  Morse  sounder.  This  galvanometer  is  a  very  sensitive  re- 
ceiver, but  it  is  very  fatiguing  to  the  operator  to  watch  the  motion 
of  the  spot  of  light. 

The  siphon  recorder  is  another  very  sensitive  receiving  instru- 
ment invented  by  Sir  William  Thomson.     This  instrument  is 
Fig,  440.  shown  in  Figure  440.   The 

pen  is  a  fine  glass  tube  n 
bent  in  the  form  of  a  si- 
phon. The  short  arm  of 
this  siphon  dips  into  a 
reservoir  of  ink  m,  and  the 
long  arm  is  bent  at  right 
angles  so  as  nearly  to  touch 
a  ribbon  of  paper  a,  whicli 
is  moved  along  at  a  uni- 
form rate  by  machinery. 

The  pen  is  hung  on  a 
thread  //',  and  is  guided 
by  a  thread  k  i  ft,  which  is 
attached  to  a  small  coil 
b.  This  coil  is  connected 
with  the  cable  by  means 
of  the  wires  /,/'.  It  is  sus- 
pended by  a  double  thread  c  from  the  points/,  and  is  held  steady 
by  the  weights  w,  w',  attached  to  it  by  the  threads/,/'.  The 
coil  is  hung  over  an  iron  core  a,  which  it  does  not  touch,  and 
in  the  magnetic  field  between  the  two  poles  of  a  powerful  electro- 
magnet, not  shown  in  the  diagram.  This  electro-magnet  is  kept 
active  by  means  of  a  magneto-electrical  machine,  which  also 
drives  a  small  electrical  machine,  which  charges  the  ink  in  the 
reservoir  and  the  paper  with  unlike  electricities.  The  attraction 
of  these  electricities  maintains  a  steady  flow  of  ink  through  the 
pen,  and  causes  it  to  escape  from  the  point  in  minute  drops 
which  make  a  straight  line  on  the  paper  when  the  pen  is  still. 
As  the  direction  of  the  current  in  the  cable  is  reversed,  the  little 
coil  b  turns  in  the  magnetic  field  a  little  to  the  right  or  left, 


NATURAL   PHILOSOPHY.  407 

according  to  the  direction  of  the  current,  on  a  vertical  axis.  As 
the  coil  turns,  it  alternately  pulls  and  releases  the  thread  A  ik, 
and  causes  the  end  of  the  siphon  pen  next  to  the  paper  to  swing 
a  little  to  the  right  and  left,  according  to  the  direction  in  which 
the  coil  turns.  As  the  end  of  the  pen  moves  to  the  right  and 
left,  the  ink  flowing  from  it  makes  a  waving  line  on  the  paper, 
which  indicates  every  change  in  the  current  of  the  cable.  The 
movements  of  the  end  of  the  pen  thus  recorded  on  the  paper  cor- 
respond to  the  movements  of  the  galvanometer  needle  indicated 
by  the  spot  of  light  reflected  from  the  little  mirror. 

483.  Varley*s  Method  of  working  the  Cable  with  Condensers. 
—  In  Varley's  method,  the  rapid  discharge  of  the  cable  is 
effected  by  means  of  condensers. 

The  general  arrangement  of  the  condensers  and  the  other 
parts  of  the  cable  apparatus  is  shown  in  Figure  441.  C  and  C' 
are  two  condensers,  one  at  each  end  of  the  cable.  One  of  the 
coatings  of  each  of  these  condensers  is  connected  with  the 
cable,  and  the  other  coating  with  the  apparatus  on  land.  D  and 
U  are  metallic  buttons  turning  on  pivots  at  o  and  o'  between 
two  metallic  discs  m,  n  and  m',  n' .  m  and  m'  are  connected 
with  the  levers  L  and  L'  of  the  keys  ;  «  and  «'  are  connected 
with  the  coils  b  and  b'  of  the  receiving  instruments,  which  may 
be  either  galvanometers  or  siphon  recorders.  The  other  end  of 
each  of  these  coils  is  connected  with  the  earth.  The  levers 
E,  E'  of  the  keys  are  also  connected  with  the  earth.  M  and  M' 
are  the  batteries,  the  positive  poles  of  which  are  connected  with 
the  bars  A,  A'  of  the  keys,  and  the  negative  poles  with  the  bars 
B,B'.  The  button  D  is  arranged  for  transmitting  a  message, 
and  the  button  D'  for  receiving  it. 

On  depressing  the  lever  E  of  the  key  at  the  sending  station, 
positive  electricity  is  sent  to  the  land  coating  of  the  condenser 
C.  This  positive  electricity  holds  negative  electricity  upon  the 
cable  coating  of  this  condenser,  and  drives  positive  electricity 
to  the  cable  coating  of  the  condenser  C',  which  in  turn  holds 
negative  electricity  on  the  other  coating  of  the  condenser,  and 
drives  positive  electricity  into  the  ground,  through  the  coil  b'  of 
the  receiving  instrument  at  the  receiving  station. 

On  depressing  the  lever  Z,  negative  electricity  is  sent  to  the 
land  coating  of  the  first  condenser,  and,  by  a  series  of  inductive 


NATURAL   PHILOSOPHY. 


actions  similar  to  those  just  described,  negative  electricity  is  sent 
Fig.  441.  _     .  —  -  from  the  land  coat- 

~  'n 


C'  through  the  coil 
b  to  the  ground. 
Thus,  by  alternately 
i— I  depressing  the  keys 
E  and  L,  positive 
and  negative  elec- 
tricity are  alternately  sent  through  the  coil  b', 
although  no  electricity  passes  through  the  cable 
from  the  battery.  On  breaking  contact  with  the 
battery  by  releasing  the  lever  of  the  key,  the 
land  coating  of  the  condenser  C  is  discharged  to 
earth  through  0,  m,  L,  A,  and  E;  the  land  coat- 
ing of  C'  through  <?',  «',  and  b'j  and  the  cable 
coatings  of  the  condensers  discharge  into  each 
other  through  the  cable,  and  so  promptly  dis- 
charge the  cable.  As  contact  with  the  battery 
by  the  key  is  broken  immediately  after  it  is 
made,  the  discharge  which  follows  of  the  oppo- 
site electricity  from  the  land  coating  of  the  con- 
denser C'  through  the  receiving  instrument 
promptly  checks  the  movement  produced  by 
the  first  current.  Hence  the  signals  are  given 
promptly  and  sharply. 

On  some  lines  a  condenser  is  used  at  only 
one  end  of  the  cable.  With  the  condensers, 
messages  may  be  transmitted  on  an  Atlantic  cable 
at  the  rate  of  17  words  a  minute. 

484.  Duplexing  the  Cable.  —  The  cable  may 
be  duplexed  by 
placing  the  receiv- 
ing instrument  on 
a  bridge,  as  shown 
in  Figure  442.  The 
battery  and  key  are 
arranged  as  before. 
C  is  the  sending 


NATURAL    PHILOSOPHY. 


409 


condenser  and  E  the  receiving  condenser.  The  circuit  divides 
at  A'  into  two  portions,  which  pass  around  the  bridge  B  D. 
The  four  branches  of  the  bridge  are  A  B,  B  B',  A  D.  and  D  F. 
The  receiving  coil  6,  as  well  as  the  receiving  condenser  E,  is  on 
the  bridge.  The  resistance  boxes,  «/,  xy  y,  are  adjusted  so  that 
none  of  the  outgoing  current  shall  cross  the  bridge  B  D.  The 
resistance  of  y  is  made  as  large  as  that  of  the  cable,  and  the  con- 
denser G  connected  with  it  is  made  to  have  as  great  a  capacity 
as  the  cable.  The  condenser  is  arranged  "in  such  a  way  that  it 
shall  discharge  itself  at  the  same  rate  as  the  cable  on  breaking 
contact  at  the  key,  in  order  that  the  discharge  from  the  condenser 

Fig.  442. 


may  exactly  balance  that  from  the  cable  on  breaking  contact,  so 
that  there  may  be  no  movement  of  the  receiving  instrument. 

The  arrangement  of  the  bridge  at  the  other  end  of  the  cable 
is  precisely  the  same  as  at  this.  The  Direct  United  States 
Cable  has  been  successfully  duplexed.  The  only  thing  needed 
to  duplex  successfully  any  cable  is  to  make  the  artificial  line 
D  G  F  exactly  equal  to  the  cable  in  resistance,  capacity,  and 
rate  of  discharge.  The  condenser  F  represents  the  one  at  the 
other  end  of  the  cable. 

F.  TRANSMISSION  OF  POWER  BY  MEANS  OF  ELECTRICITY. 

485.  Electro- Motors.  —  The  current  produced  by  moving 

a  magnet  near  a  wire,  or  a  wire  near  a  magnet,  always 

opposes  the  motion  which  produces  it  ;  that  is  to  say,  it 


4io        -  NATURAL  PHILOSOPHY. 

tends  to  produce  motion  in  the  opposite  direction.  Hence 
if  a  current  of  electricity  from  any  external  source  were 
sent  through  the  coils  of  a  magneto-electrical  machine  in 
the  direction  of  the  one  produced  in  these  coils  by  the  ac- 
tion of  the  machine,  it  would  cause  the  cylinder  to  revolve 
in  the  opposite  direction  to  that  in  which  it  must  be  turned 
to  produce  a  current.  Hence  electricity  when  sent  through 
the  coils  of  such  a  machine  becomes  a  source  of  power. 

A  machine  driven  by  electricity  is  called  an  electro-motor, 
There  are  various  forms  of  electro-motors,  but  the  most  effi- 
cient are  those  constructed  on  the  principle  of  the  reversibil- 
ity of  dynamo-electrical  machines.  It  is  proposed  to  employ 
electricity  as  a  motive  power  for  a  great  variety  of  purposes. 

Companies  have  been  formed  to  develop  electric  cur- 
rents at  one  or  more  centres  in  cities,  and  send  them 
through  wires  laid  in  the  streets  to  the  houses,  to  be  used 
for  a  variety  of  domestic  purposes,  such  as  driving  clocks, 
working  sewing-machines,  pumping  water,  etc. 

It  is  thought  that  electricity  will  be  found  to  be  the 
medium  by  which  power  can  be  most  efficiently  and 
economically  transmitted  to  a  distance.  For  instance, 
when  water-power  is  abundant  in  places  remote  from  the 
localities  where  the  power  is  needed,  the  energy  of  the 
water  may  be  converted  into  that  of  electricity  by  means 
of  dynamo-electrical  machines,  then  the  electricity  con- 
ducted to  the  distant  points  through  wires,  and  used  as  a 
source  of  power  with  similar  dynamo-electrical  machines. 

G.   ELECTRO-THERMAL  ACTION. 

486.  Thermo- Electric  Piles.  —  When  two  metals  are 
Fig.  443.  soldered  together,  so  as  to  form  a  closed  cir- 
cuit, as  shown  in  Figure  443,  and  one  of  the 
junctions  is  heated  more  than  the  other,  a 
current  flows  around  the  circuit.  The  direc- 
tion and  strength  of  the  current  vary  with 


NATURAL   PHILOSOPHY.  411 

the  metals  used.  Such  a  combination  of  two  metals  is 
called  a  thermo-electric  pair.  Antimony  and  bismuth  form 
the  best  combination  among  the  metals.  In  this  combi- 
nation the  current  flows  across  the  heated  junction  from 
the  bismuth  to  the  antimony, 

With  a  single  pair  of  metals  only  a  feeble  current  is 
obtained.  These  pairs  may  be  combined  so  as  to  form 
batteries,  or  piles.  The  pairs  are  soldered  Fig.  444. 

together  at  alternate  ends,  as  shown  in 
Figure  444.  Several  hundred  pairs  are 
often  combined  in  a  pile. 

The  least  difference  of  temperature 
between  the  ends  of  such  a  pile  gives 
rise  to  a  current.  When  used  with  a  delicate  galvanometer 
the  thermo-electric  pile  is  an  exceedingly  sensitive  differ- 
ential thermometer.  No  current  is  obtained  from  the 
thermo-electric  pile  when  the  two  faces  are  heated  equally. 

487.  The  Thermal  Balance.  —  It  is  found  that  the  resistance 
of  a  conductor,  as  a  rule,  increases  as  its  temperature  rises.  Pro- 
fessor Langley  has  taken  advantage  of  this  fact  to  construct  a 
thermal  instrument  of  remarkable  sensibility,  called  tint  thermal 
balance.  He  introduces  a  number  of  strips  of  steel,  ^  of  an  inch 
wide  and  -%-fc$  of  an  inch  thick,  side  by  side,  into  one  of  the  two 
branches  of  a  circuit.  The  two  branches  are  adjusted  so  as  to 
divide  the  current  equally  when  the  steel  strips  are  at  the  same 
temperature  as  the  rest  of  the  circuit,  and  are  connected  to  the 
coils  of  a  differential  galvanometer.  On  heating  or  cooling 
these  strips  of  steel,  their  resistance  is  either  increased  or 
diminished,  the  equality  of  the  currents  in  the  two  branches 
of  the  circuit  is  destroyed,  and  the  needle  of  the  galvanometer 
is  deflected.  This  instrument  is  much  more  delicate  than  the 
thermopile  described  above,  and  what  is  even  more  important, 
is  far  more  rapid  in  its  action.  It  will  indicate  a  change  of  tem- 
perature of  -5^3-0  Part  °f  a  Fahrenheit  degree.  Mounted  in  a 
reflecting  telescope,  it  will  indicate  the  heat  from  a  man  or 
other  animal  in  a  field  many  yards  distant. 


412  NATURAL   PHILOSOPHY. 

488.  The  Development  of  Heat  by  means  of  the  Current. 
—  Whenever  a  powerful  current  of  electricity  flows  through 
a  wire  it  heats  it.     The  finer  the  wire,  and  the  lower  the 
conducting  power  of  the  material  of  which  it  is  composed, 
the  more  intense  the  heat  developed.     The  more  powerful 
the  current  employed,  the  more  intense  the  heat  obtained 
with  the  same  conductor.     Fine  wires  of  the  most  refrac- 
tory metals  are  heated  white-hot,  and  even  fused,  on  the 
passage  of  powerful  currents. 

489.  Electric  Illumination  by  Incandescence.  —  There  has 
been  for  a  long  time  an  effort  to  make  electricity  available 
as  a  source  of  light,  and  at  last  the  many  practical  diffi- 
culties that  have  been  met  with  seem  to  have  been  nearly, 
if  not  quite,  surmounted.     Illumination  by  means  of  a  poor 
conductor  heated  to  a  white  heat  on  the  passage  of  the 
current,  is  called  illumination   by  incandescence.     The  great 
difficulty  encountered  in  illumination  by  incandescence  is 
that  the  conductor  which  is  heated  to  incandescence  by 
the  current  is  also  apt  to  be  destroyed  by  the  current. 
Even  so  refractory  a  substance  as  platinum  is  very  likely 
to  fuse  when  heated  to  incandescence.     Hence  there  is  no 
dependence  to  be  placed  upon  a  lamp  in  which  a  metallic 
wire  is  heated  to  incandescence  by  the  current.     If  the 
current  is  sent  through  a  very  thin  rod  of  carbon,  the  car- 
bon becomes  heated  to  incandescence ;  but  at  the  high 
temperature  the  carbon  is  liable  to  be  destroyed  by  com- 
bining with  the  oxygen  of  the  air.     Even  when  the  carbon 
is  placed  in  an  exhausted  receiver,  or  in  one  which  has 
been  first  exhausted  of  air  and  then  filled  with  nitrogen 
or  some   other  gas  which  is  a  non-supporter  of  combus- 
tion, the  carbon  filament  is  liable  to  disintegration. 

490.  The  Edison  Lamp.  —  The  Edison  lamp  for  incan- 
descence is  shown,  in  section,  in  Figure  445.     The  upper 
portion   of  the  lamp  is  a  glass  globe,  from  which  the  air 
has  been  exhausted,  and  which  is  hermetically  sealed.     In 


NATURAL    PHILOSOPHY. 


413 


the  centre  of  this  globe  is  the  carbon  filament,  bent  in 
the  form  of  a  ring.  The  ends  of  this  filament  are  held  in 
little  clamps,  which  are  connected  with  Fig.  445. 

the  platinum  wires  which  pass  through 
the  glass  of  the  smaller  globe  under  the 
ring,  and  thence  out  through  the  bottom 
of  the  lamp,  where  they  are  connected 
with  the  wires  of  the  circuit. 

The  permanent  success  of  this  and 
similar  lamps  for  illumination  depends 
solely  upon  whether  the  carbon  filament 
is  found,  in  practice,  to  be  sufficiently 
durable.  The  Edison  filament  is  con- 
structed of  bamboo-wood.  The  bamboo 
filament,  before  it  is  bent  and  carbon- 
ized, is  shown  in  Figure  446.  It  is  from 
five  to  seven  inches  in  length,  and  from 
3*5  to  3*2  of  an  inch  in  diameter.  It  is  first 
worked  to  a  uniform  size  throughout, 
and  then  bent  into  a  ring  and  carbonized  under  pressure. 
The  resistance  of  the  loop  is  from  100  to  300  ohms,  and 
the  amount  of  light  that  can  be  safely  obtained  from  it 
varies  from  2  to  10  candles. 

Fig.  446. 


These  lamps  will  be  arranged  in  the  houses  just  as  gas- 
jets  are  now,  and  electricity  will  be  conducted  to  them  by 
wires  in  the  streets,  just  as  gas  is  conducted  to  the  gas-jets 
by  pipes  in  the  streets. 

Edison's  plan  is  to  measure  the  electricity  used  in  each 
house  by  a  kind  of  voltameter,  in  which  sulphate  of  copper 
is  decomposed  instead  of  sulphuric  acid.  The  copper  is 
deposited  on  one  of  the  electrodes  and  so  increases  its 
weight.  The  increase  in  weight  of  the  plate  will  show  the 


414 


NATURAL    PHILOSOPHY. 


amount  of  electricity  which  has  passed  through  the  instru- 
ment. 

Illumination  by  incandescence  is  especially  adapted  for 
lighting  rooms  of  the  ordinary  size, 

491.  The  Voltaic  Arc.  —  If  two  pencils  of  coke  carbon 
are  introduced  into  a  circuit  through  which  a  powerful  cur- 
rent of  electricity  is  passing  so  as  to  be  in  contact  at  their 
ends,  on  separating  these  pencils 'a  little,  intense  light  and 
heat  will  be  developed  at  the  point  of  separation  (Figure 
447).  The  ends  of  the  pencils  will  be  heated  white-hot, 

Fig.  447- 


and  they  will  be  connected  by  a  luminous  bridge.  This 
bridge  is  called  the  voltaic  arc.  The  light  and  heat  of  the 
voltaic  arc  are  the  most  intense  that  can  be  obtained  by 
artificial  means. 

If  the  carbons  are  separated  far  enough  to  stop  the 
current,  it  will  not  start  again  till  they  have  been  again 
brought  in  contact.  After  the  current  has  been  started,  it 
will  continue  to  flow  after  the  carbons  are  separated,  pro- 
vided they  are  not  separated  too  far.  The  reason  the  cur- 
rent will  continue  to  flow  after  the  carbons  have  been 
separated,  though  it  will  not  begin  to  flow  till  they  have 
been  brought  into  contact,  is  this.  As  the  carbons  begin 


\.\  I  1   KAL    PHILOSOPHY. 


415 


to  separate,  the  current  which  is  passing  detaches  little 
particles  from  each  of  them  and  transfers  these  to  the 
other  carbon,  and  so  bridges  over  the  space  between  the 
points  with  carbon  dust.  The  air  thus  filled  with  par- 
ticles of  carbon  offers  less  resistance  to  the  current  than 
the  air  free  from  carbon  dust  which  separates  the  points 


before  they  are  brought  into  contact.  Another  reason  is 
that  heated  air  offers  less  resistance  than  cold  air.  The 
intense  heat  of  the  voltaic  arc  is  due  to  the  resistance 
which  the  current  encounters  in  the  space  between  the 
carbon  points. 

The  end  of  the  positive  carbon  becomes  concave,  and 
that  of  the  negative  carbon  pointed,  as  shown  in  Figure 


416 


NATURAL    PHILOSOPHY. 


Fig.  449- 


448.     Both  carbons  are  consumed,  but  the  positive  more 
rapidly  than  the  negative. 

492.  Illumination  by  the  Voltaic  Arc.  —  In  order  to  ob- 
tain illumination  by  the  voltaic  arc,  a  lamp  is  needed  to 
keep  the  carbons  all  the  time  at  the  right  distance  apart, 
and  to  bring  the  points  together,  in  case  the  current  should 
stop,  and  then  to  separate  them  again  when  the  current 
has  started. 

Illumination  by  the  voltaic  arc 
is  too  intense  for  rooms  of  the 
ordinary  size,  but  is  especially 
adapted  for  out-door  illumina- 
tion, and  for  large  halls  and 
workshops. 

493.  Foucaulfs  Regulator.  — 
When  it  is  necessary  to  keep 
the  light  all  the  time  at  the  same 
point,  as  in  the  lantern  for  pro- 
jection, there  is  needed  a  lamp 
which  shall  move  each  carbon  at 
the  rate  at  which  it  is  consumed. 
The  best  lamp  for  this  purpose  is 
Foucaulfs  regulator.  This  lamp  is 
shown  in  Figure  449.  The  points 
are  moved  by  means  of  clock-work, 
which  is  so  constructed  that  it  can 
be  made  to  move  the  points  either 
together  or  apart.  The  clock-work 
is  controlled  by  an  electro-magnet 
E  by  means  of  the  lever  F.  The 
current  passes  through  the  coil  of 
this  electro-magnet  on  its  way  to 
the  carbons.  When  the  carbons 
become  too  far  apart,  the  current 
is  weakened,  the  lever  F  is  re- 
leased, and  the  clock-work  is  made 
to  turn  so  as  to  move  the  carbons  together.  When  the  carbons 


NATURAL    PHILOSOPHY. 


4'7 


come  too  near  together,  the  current  becomes  strong  enough  to 
draw  the  lever  down,  and  this  causes  the  clock-work  to  turn  so 
as  to  separate  the  points.  When  the  points  are  at  just  the  right 
distance  apart,  the  lever  F  is  held  in  such  a  position  as  to  stop 
Fig.  45o.  the  clock-work  entirely. 

494.  The  Brush  Lamp.  —  For  ordinary  il- 
lumination, it  is  not  necessary  that  the  light 
should  be  maintained  at  the  same  point.  One 
of  the  best  lamps  for  purposes  of  general 
illumination  by  the  voltaic  arc  is  the  Brush 
la»tp,  which  is  shown  in  Figure  450.  The 
upper  carbon  is  fastened  to  a  rod /"which  passes 
loosely  through  the  centre  of  the  hollow  iron 
core  d  of  the  coil  a.  This  core  is  partially 
supported  by  the  adjustable  springs  ee.  A  me- 
tallic washer  h  surrounds  the  rod  just  below  the 
core  d.  This  disc  rests  on  one  side  of  the  lift- 
ing finger^  (Figure  451)  attached  to  the  core 
d.  Just  above  the  washer,  on  the  other  side,  is 


the  head  of  the  screw  x. 
The  current  which  passes 
between  the  carbon  points 
also  passes   through   the 
coil  at  the   top.      When 
the  current  becomes  too  strong  by  reason 
of   the  carbons  coming  too  near  together, 
the  core  is  pulled  up  into  the  coil,  and  the 

Fig.  45'- 


Fig.  452- 


4l8  NATURAL   PHILOSOPHY. 

lifting  finger  tilts  the  washer  (Figure  452)  so  as  to  clamp  the 
rod  that  holds  the  upper  carbon,  and  it  at  the  same  time  raises 
the  rod  till  stopped  by  the  screw-head  on  the  opposite  side. 
When  the  current  becomes  too  feeble  by  the  carbons  getting 
too  far  apart,  the  core  is  released,  the  washer  is  dropped,  and 
the  rod  slides  freely  through  it. 

H.   RADIANT  MATTER. 

495.  Changes  produced  in  a  Vacuum  Discharge  by  Variation 
of  Pressure.  —  If  the  terminals  of  a  vacuum  tube  are  connected 
with  a  large  induction  coil,  and  the  tube  is  arranged  so  that  it 
may  be  gradually  exhausted  by  means  of  a  mercurial  pump, 
when  the  pressure  has  been  reduced  to  a  small  fraction  of  a 
millimetre  the  whole  tube  will  be  filled  with  a  bright  light.     As 
the  exhaustion  proceeds,  the  luminous  stream  breaks  up  into  a 
number  of  discs  of  light  called  strice. 

The  stratification  of  the  discharge  varies  greatly  under  dif- 
ferent circumstances.  Some  of  the  forms  of  stratification  are 
shown  in  Figures  453  and  454. 

496.  Crookes^s   Discovery. —  Mr.  William  Crookes  has  dis- 
covered that  when  the  exhaustion  of  a  vacuum  tube  is  carried 
considerably  beyond  that  point  which  gives  the  best  striae  and 
luminous  effects,  a  new  set  of  phenomena  not  hitherto  observed 
are  produced  ;  and  the  residual  gas  develops  so  many  new  prop- 
erties that  he  considers  himself  justified  in  saying  that  gas,  when 
at  these  low  pressures,  may  be  regarded  as  matter  in  a  fourth  or 
ultra-gaseous  state.     To  this  he  has  given  the  name  of  Radiant 
Matter. 

According  to  Mr.  Crookes,  the  states  of  matter  are  four,  as 
follows :  — 

1.  Solid. 

2.  Liquid. 

3.  Gaseous. 

4.  Radiant. 

The  pressure  at  which  these  new  phenomena  are  best  seen  is 
about  one  millionth  of  an  atmosphere.  This  is  about  ^fa  of 
the  pressure  of  an  ordinary  vacuum  tube.  The  effect  of  the 


NATURAL   PHILOSOPHY. 
F>K.  453- 


« 

— . 


420 


NATURAL    PHILOSOPHY. 
F>g-  454- 


NATURAL   PHILOSOPHY.  421 

diminution  of  the  pressure  upon  a  gas  is  to  increase  the  dis- 
tance between  the  molecules  and  the  length  of  their  free  paths. 

Suppose  a  box  containing  a  cubic  foot  of  hydrogen  at  the 
ordinary  density  were  opened  in  a  cubical  room  measuring  100 
feet  each  way  and  being  a  perfect  vacuum.  The  hydrogen 
would  fill  the  room,  and  its  rarefaction  would  represent  that  of 
a  pressure  of  one  millionth  of  the  atmosphere.  The  molecules 
of  the  hydrogen  were  originally  about  one  seven-millionth  of  an 
inch  apart,  and  the  mean  length  of  their  free  paths  about 
aWinnr  °^  an  'ncn-  After  being  rarefied  to  a  millionth  of  the 
atmospheric  pressure,  the  molecules  will  be  one  seventy-thou- 
sandth of  an  inch  apart,  and  the  mean  length  of  their  free  paths 
will  be  about  four  inches. 

Were  a  cubic  foot  of  this  rarefied  hydrogen  opened  into  a 
second  exhausted  room  of  the  same  dimensions  as  the  first,  the 
rarefaction  would  be  increased  a  millionfold.  The  molecules 
would  now  be  about  one  seven  hundredth  of  an  inch  apart,  and 
the  mean  length  of  their  free  paths  about  sixty  miles.  In  this 
state  of  exhaustion,  which  is  about  a  million  times  beyond  that 
attainable  by  a  good  mercurial  pump,  there  are  still  no  less  than 
340  million  molecules  in  every  cubic  inch. 

Were  the  rarefaction  increased  a  millionfold  by  transferring 
a  cubic  foot  of  the  gas  from  the  second  room  to  a  third  ex- 
hausted room  of  the  same  dimensions  as  the  first,  the  molecules 
would  be  about  one  seventh  of  an  inch  apart,  and  their  free 
paths  about  60  million  miles  long.  It  would  take  a  molecule  of 
hydrogen,  which  ordinarily  moves  about  three  times  as  fast 
as  a  cannon  ball,  nearly  two  years  to  traverse  its  free  path 
under  these  circumstances. 

497.  The  Dark  Space  at  the  Negative  Pole.  —  In  all  well- 
exhausted  vacuum  tubes  a  small  dark  space  surrounds  the  nega- 
tive pole  during  the  discharge.  Crookes  found  that  the  dark 
space  increases  in  length  as  the  exhaustion  proceeds.  He  illus- 
trated the  effect  of  change  of  pressure  on  the  dark  space  by  the 
use  of  the  tube  shown  in  Figure  455.  The  negative  pole  at 
the  centre  was  in  the  form  of  a  metallic  disc.  The  two  end 
poles  were  connected  together  and  made  the  positive  terminal. 
With  a  rather  low  exhaustion  the  dark  space  extended  only 
a  little  way  each  side  of  the  pole,  but  as '  the  exhaustion  was 


422 


NATURAL    PHILOSOPHY. 


improved  the  dark  space  extended  till  it  became  an  inch  in 
length. 

He  accounts  for  the  increase  as  follows :   Molecules  of  gas 
are  driven  off  from  the  negative  pole,  and  as  long  as  thev  do 

•       Fie.  4SS. 


not  come  into  collision  with  any  other  molecules,  they  do  not 
produce  any  light.  The  space  over  which  they  travel  without 
collision  will  be  dark. 

When,  by  diminishing  the  pressure,  the  mean  free  path  is 
lengthened,  the  dark  space  increases. 


498.    Phosphorescence   developed  by  Radiant  Matter.  —  We 
have  seen  that  the  radiant  matter  within  the  dark'space  develops 


NATURAL    PHILOSOPHY.  423 

luminosity  only  when  the  molecules  dart  against  other  molecules 
of  the  residual  gas.  If  the  exhaustion  is  carried  to  a  sufficient 
point,  there  will  be  no  collision  of  the  molecules  of  the  gas,  the 
molecules  being  arrested  only  on  striking  against  the  sides  of 
the  tube.  When  the  molecules  in  this  condition  strike  against 
any  suitable  solid  they  develop  a  greater  or  less  degree  of  phos- 
phorescence, according  to  the  nature  of  the  body.  Crookes 
finds  that  very  many  solids  become  phosphorescent  under  the 
molecular  blows  of  radiant  matter,  and  that  diamond  is  the  most 
sensitive  of  all  substances. 

He  supported  a  diamond  on  a  little  stand  in  the  centre  of  a 
globe,  as  shown  in  Figure  456,  and  directed  the  molecular  dis- 
charge upon  it  from  below  by  means  of  the  terminals  seen  at 
the  right  and  the  left  in  the  figure.  In  a  darkened  room  the 
diamond  was  as  bright  as  a  candle. 

Fig.  457- 


499.  Radiant  Matter  travels  in  Straight  Lines.  —  Figure 
457  represents  a  V-shaped  vacuum  tube,  with  a  pole  at  each 
extremity.  On  making  the  pole  at  the  right  negative  and  the 
one  at  the  left  positive,  the  whole  of  the  right  arm  was  flooded 
with  green  light,  but  at  the  bottom  it  stopped  sharply  and  would 
not  turn  the  corner  to  get  into  the  left  side.  When  the  current 


424  NATURAL    PHILOSOPHY. 

was  reversed  and  the  left  pole  made  negative,  the  green  changed 
to  the  left  side,  always  following  the  negative  pole,  and  leaving 
the  positive  side  with  scarcely  any  luminosity. 

To  produce  the  ordinary  phenomena  exhibited  by  vacuum 
tubes,  it  is  customary,  in  order  to  bring  out  the  striking  contrasts 
of  color,  to  bend  the  tubes  into  very  elaborate  designs.  The 
luminosity  caused  by  the  phosphorescence  of  the  residual  gas 
follows  all  the  convolutions  into  which  skilful  glass-blowers  can 
manage  to  twist  the  glass.  The  negative  pole  being  at  one  end 
458. 


and  the  positive  pole  at  the  other,  the  luminous  phenomena 
seem  to  depend  more  on  the  positive  than  on  the  negative  at  the 
ordinary  exhaustion  hitherto  used  to  get  the  best  phenomena  of 
vacuum  tubes.  But  at  a  very  high  exhaustion  the  phenomena 
noticed  in  ordinary  vacuum  tubes  when  the  induction  spark 
passes  through  them,  —  an  appearance  of  cloudy  luminosity  and 
of  stratifications,  —  disappear  entirely.  No  cloud  or  fog  what- 
ever is  seen  in  the  body  of  the  tube,  and  with  such  a  vacuum  as 
is  used  in  these  experiments  the  only  light  observed  is  that 
from  the  phosphorescent  surface  of  the  glass.  Figure  458 


NATURAL    PHILOSOPHY.  425 

represents  two  bulbs,  alike  in  shape  and  position  of  poles,  the 
only  difference  being  that  one  is  at  an  exhaustion  equal  to  a  few 
millimetres  of  mercury,  —  such  a  moderate  exhaustion  as  will 
give  the  ordinary  luminous  phenomena,  —  whilst  the  other  is 
exhausted  to  about  the  millionth  of  an  atmosphere.  First 
connect  the  moderately  exhausted  bulb  A  with  the  induction 
coil,  and  make  the  pole  at  one  side,  «,  always  negative,  and  the 
other  poles  with  which  the  bulb  is  furnished  positive  in  succes- 
sion. As  the  position  of  the  positive  pole  is  changed,  the  line 
of  violet  light  joining  the  two  poles  changes,  the  electric  current 
always  choosing  the  shortest  path  between  the  two  poles,  and 
moving  about  the  bulb  as  the  position  of  the  wires  is  altered. 

Try  the  same  experiments  with  the  highly  exhausted  globe 
B.  Make  a'  the  negative  pole,  as  before.  This  pole  has  a  con- 
cave surface.  The  molecular  rays  will  cross  in  the  centre  of 
the  bulb,  and,  diverging  thence,  will  fall  on  the  opposite  side, 
producing  a  circular  patch  of  green  phosphorescent  light.  The 
position  of  the  spot  of  light  remains  the  same  whether  b,  c,  or  d 
is  made  the  positive  pole.  In  a  very  high  vacuum,  no  matter 
what  may  be  the  position  of  the  positive  pole,  the  radiant  matter 
always  darts  off  in  straight  lines  from  the  negative  pole,  the  rays 
being  always  perpendicular  to  the  surface. 


500.  Shadows  cast  by  Radiant  Matter.  — \n  Figure  459  is 
shown  a  pear-shaped  vacuum  tube  with  the  negative  pole  a  at 
the  small  end.  In  the  middle  of  the  tube  is  an  aluminium  cross 
b.  The  molecular  rays  from  a  which  reach  the  opposite  end  of 
the  tube  develop  phosphorescence,  but  a  portion  of  the  rays  are 
intercepted  by  the  cross,  whose  shadow  is  seen  on  the  end  of 


426 


NATURAL    PHILOSOPHY. 


the  tube.     The  portion  of  the  end  of  the  tube  behind  the  cross 
is  shielded  from  the  molecular  blows,  and  so  remains  dark. 

Fig.  460. 


Fig.  461 


501.  Molar  ITotion  produced  by  Radiant  Matter.  —  In  Fig- 
ure 460  is  shown  a  highly  exhausted  vacuum  tube,  in  the  centre 
of  which  is  a  glass  railway.  A  little  wheel  with  broad  mica 
paddles  rests  on  this  railway.  At  each  end  of  the  tube  and  a 
little  above  the  centre  there  is  an  aluminium  pole.  One  of  the 
poles  is  made  the  negative  terminal  and  the  other  the  positive. 
The  stream  of  radiant  matter  from  the  negative  terminal  strikes 
the  upper  vanes  of  the  little  paddle-wheel  and  causes  it  to  roll 
along  the  railway.  On  the  reversal  of  the  poles,  the  wheel  is 
stopped  and  made  to  reverse  its  path.  If  the  tube  is  gently 
inclined,  the  force  of  the  radiant  stream  is  seen  to  be  sufficient 
to  drive  the  wheel  up  hill. 

In  Figure  461  is  shown  a  little  fly  in  the 
centre  of  a  highly  exhausted  bulb.  The  fly 
consists  of  four  arms  of  aluminium,  each 
carrying  at  the  end  a  thin  aluminium  disc, 
coated  on  one  side  with  mica.  The  fly  turns 
upon  a  hard  steel  point,  which  is  connected 
with  the  negative  pole  of  the  induction  coil. 
The  positive  terminal  is  at  the  top  of  the  bulb. 
With  a  pressure  of  only  a  few  millimetres,  a 
halo  of  velvety  violet  light  settles  on  the  me- 
tallic sides  of  the  discs,  the  mica  sides  remaining 
dark.  As  the  pressure  diminishes,  a  dark  space 
separates  the  violet  halo  from  the  metallic 
disc.  With  a  pressure  of  half  a  millimetre, 
the  dark  space  extends  to  the  glass,  and  the 
fly  begins  to  rotate,  the  metallic  discs  moving 


NATURAL    PHILOSOI'IIV. 


427 


backward.  As  we  continue  the  exhaustion,  the  dark  space 
widens  out  and  appears  to  flatten  itself  against  the  glass.  The 
rotation  now  becomes  very  rapid.  The  fly  is  turned  by  the 
reaction  of  the  molecules  as  they  are  shot  from  the  discs. 


Fig.  462. 


502.  Deflection  of  Radiant  Matter  by  a  Magnet.  —  In  Figure 
462  is  shown  a  highly  exhausted  tube  with  its  negative  terminal 
at  N  and  its  positive  terminal  at  P.  There  is  a  long  phospho- 
rescent screen  be  passing  down  the  centre  of  the  tube.  In  front 
of  the  negative  pole  is  a  mica  plate  bd  with  a  hole  e  in  its 
centre.  On  turning  on  the  electric  current,  a  line  of  phosphores- 
cent light  is  seen  along  the  screen  in  the  direction  ef.  This 
line  of  light  reveals  the  path  of  the  radiant  stream.  A  powerful 
horseshoe  magnet  is  now  placed  under  the  tube,  and  the  line 
of  light,  eg,  becomes  curved  under  the  magnetic  influence, 
waving  about  like  a  flexible  wand  as  the  magnet  is  moved  to 
and  fro. 

Fig.  463- 


"This  action  of  the  magnet  is  very  curious,  and,  if  carefully 
followed  up,  will  elucidate  other  properties  of  radiant  matter. 
Figure  463  represents  a  tube  exactly  similar,  but,  having  at  one 
end  a  small  potash  tube,  which,  if  heated,  will  slightly  injure  the 


428  NATURAL    PHILOSOPHY. 

vacuum.  When  the  induction  current  is  turned  on,  the  ray  of 
matter  is  seen  tracing  its  trajectory  in  a  curved  line  along  the 
screen,  under  the  influence  of  the  horseshoe  magnet  beneath. 
Let  us  observe  the  shape  of  the  curve.  The  molecules  shot 
from  the  negative  pole  may  be  likened  to  a  discharge  of  iron 
bullets  from  a  mitrailleuse,  and  the  magnet  beneath  will  repre- 
sent the  earth  curving  the  trajectory  of  the  shot  by  gravitation. 
The  curved  trajectory  of  the  shot  is  accurately  traced  on  the 
luminous  screen.  Now  suppose  the  deflecting  force  to  remain 
constant,  the  curve  traced  by  the  projectile  varies  with  the  veloc- 
ity. If  more  powder  is  put  in  the  gun,  the  velocity  will  be 
greater  and  the  trajectory  flatter  ;  and  if  a  denser  resisting  me- 
dium is  interposed  between  the  gun  and  the  target,  the  velocity 
of  the  shot  will  be  diminished,  and  it  will  move  in  a  greater  curve 
and  come  to  the  ground  sooner.  The  velocity  of  this  stream  of 
radiant  molecules  cannot  well  be  increased  by  strengthening  the 
battery,  but  they  can  be  made  to  suffer  greater  resistance  in 
their  flight  from  one  end  of  the  tube  to  the  other.  In  the  ex- 
periment shown,  the  caustic  potash  is  heated  with  a  spirit  lamp, 
and  so  a  trace  more  of  gas  is  thrown  in.  Instantly  the  stream  of 
radiant  matter  responds.  Its  velocity  is  impeded,  the  magnetism 
Fig.  464.  has  l°nger  time  in  which  to  act  on  the 

individual  molecules,  the  trajectory  be- 
comes more  and  more  curved  until,  in- 
stead of  shooting  nearly  to  the  end  of 
the  tube,  the  '  molecular  bullets  '  fall  to 
the  bottom  before  they  have  got  more 
than  half-way." 

503.  Development  of  Heat  by  Radi- 
ant Matter.  —  The  bulb  (Figure  464) 
is  furnished  with  a  negative  pole  in 
the  form  of  a  cup  a.  The  rays  will 
therefore  be  projected  to  a  focus  on  a 
piece  of  iridio-platinum  b  supported  in 
the  centre  of  the  bulb.  The  induction 
coil  is  first  slightly  turned  on  so  as  not 
to  bring  out  its  full  power.  The  focus 
plays  on  the  metal,  raising  it  to  a  white 
heat.  By  bringing  a  small  magnet 


NATURAL    PHILOSOPHY.  429 

near  it  the  focus  of  heat  may  be  deflected.  By  shifting  the 
magnet  we  can  draw  the  focus  up  and  down,  or  completely  away 
from  the  metal,  so  as  to  leave  it  non-luminous.  When  we  with- 
draw the  magnet  so  as  to  let  the  molecules  have  full  play  again, 
the  metal  becomes  white-hot.  When  we  increase  the  intensity 
of  the  spark,  the  iridio-platinum  glows  with  almost  insupportable 
brilliancy,  and  at  last  melts. 

504.  The  Radiometer.  —  The  ordinary  radiometer  is  similar  in 
construction  to  the  instrument  shown  in  Figure  461.  The  discs 
of  the  fly  are  of  mica  blackened  on  one  side.  The  fly  is  usually 
supported  on  a  glass  stem.  The  bulb  is  highly  exhausted. 
When  the  radiometer  is  placed  in  the  light,  the  fly  begins  to 
rotate,  the  blackened  surfaces  of  the  discs  moving  backward. 
The  more  intense  the  light,  the  more  rapid  the  rotation.  The 
rotation  is  due  to  the  action  of  radiant  matter.  The  blackened 
sides  of  the  discs  absorb  the  radiation  better  than  the  light  ones. 
They  thus  become  more  heated,  and  repel  the  molecules  with 
greater  energy.  The  reaction  of  the  projected  molecules  is 
therefore  greater  on  the  blackened  sides  of  the  discs.  This 
excess  of  reaction  causes  the  rotation. 

It  has  been  suggested  that  the  ether  itself  may  be  merely  a 
form  of  radiant  matter,  and  that  light  and  heat  may  be  propa- 
gated through  it  by  molecular  projection. 


VII. 

METEOROLOGY. 
I. 

CONSTITUTION    OF   THE   ATMOSPHERE. 

505.  The   Term   Meteorology.  —  The    term    meteor  was 
formerly  applied   to   any   natural  phenomenon    occurring 
within   the    limits   of    the   atmosphere ;    hence   the   term 
meteorology  as  applied  to  that  branch  of  Natural  Philosophy 
which  treats  of  the  atmosphere. 

506.  The  Composition  of  the  Atmosphere.  —  The  atmos- 
phere  is  composed  chiefly  of  oxygen  and  nitrogen  in  a 
state  of  mechanical  mixture,  and  not  of  chemical  combi- 
nation.     In  every    100   volumes   of  air  there   are   nearly 
79.1   volumes  of   nitrogen   and  20.9   volumes   of  oxygen. 
Owing  to  the  tendency  of  these  two  gases  to  diffuse  into 
each  other,  and  to  the  currents  which  exist  in  the  atmos- 
phere, these  proportions  are  sensibly  the  same  in  all  parts 
of  the  globe  and  at   all   accessible  elevations  above    its 
surface. 

In  addition  to  the  oxygen  and  nitrogen,  the  atmosphere 
contains  also  a  little  carbonic  acid  and  watery  vapor. 
The,  amount  of  carbonic  acid  varies,  in  the  open  country, 
from  4  to  6  parts  in  a  thousand.  The  amount  of  moisture 
is  very  variable,  ranging  from  4  parts  in  one  hundred  to 
i  part  in  a  thousand. 

507.  The  Height  of  the  Atmosphere.  —  The  atmosphere 


NATURAL    PHILOSOPHY. 


43 ! 


is  held  to  the  earth  by  gravity,  and  it  must  terminate  at 
that  height  at  which  the  attraction  of  the  earth  is  balanced 
by  the  repulsion  of  the  particles  of  the  air.  At  the  height 
of  50  miles  the  atmosphere  is  wellnigh  inappreciable  in 
its  effect  upon  twilight.  The  phenomena  of  lunar  eclipses 
indicate  an  appreciable  atmosphere  to  the  height  of  66 
miles ;  while  the  phenomena  of  shooting  stars  and  of  the 
auroral  light  show  that  an  appreciable  atmosphere  exists 
at  the  height  of  200  or  300  miles,  and  probably  of  more 
than  500  miles,  above  the  earth's  surface. 

508.  The  Weight  of  the  Atmosphere.—  The  weight  or 
downward  pressure  of  the  air  at  any  point  is  ascertained 
by  the  use  of  the  barometer.  It  is  found  to  be  different 
at  different  parts  of  the  earth,  and  to  be  in  a  state  of  con- 
stant fluctuation  at  the  same  place.  If  we  observe  the 
height  of  the  barometer  every  hour  of  the  day,  and  then 
divide  the  sum  of  the  observed  heights  by  24,  we  obtain 
the  mean  height  for  the  day.  By  dividing  the  sum  of  the 
daily  means  for  a  month  by  the  number  of  days  in  the 
month,  we  obtain  the  mean  height  for  the  month.  By  divid- 
ing the  sum  of  the  monthly  means  for  a  year  by  12,  we 
obtain  the  mean  height  for  the  year.  If  we  divide  the  sum 
of  the  annual  means  for  a  series  of  years  by  the  number 
of  years  in  the  period,  we  obtain  the  mean  height  of  the 
barometer  for  the  place  of  observation.  This  at  Boston  is 
29.988  inches. 

Fig.  465. 


to°  30°  »»  m>  a»  itf  HP  ao»  *o»  to 

509.  The  Mean  Height  of  the  Harometer  at  Different 
Latitudes.  —  The  curve  in  Figure  465  shows  the  mean 
height  of  the  barometer  at  different  latitudes  from  80° 


432 


NATURAL    PHILOSOPHY. 


north  to  80°  south.  The  numbers  at  the  bottom  show  the 
latitude,  and  those  at  the  side  the  height  of  the  barometer 
in  inches.  The  height  at  which  the  curve  crosses  the  ver- 
tical lines  of  the  diagram  shows  the  mean  height  of  the 
barometer  at  that  latitude.  The  height  is  found  by  follow- 
ing the  horizontal  lines  to  the  left ;  and  the  latitude,  by  fol- 
lowing the  vertical  lines  to  the  bottom.  It  will  be  seen 
from  the  diagram,  that  the  mean  height  of  the  barometer 
is  greatest  at  32°  north  and  25°  south  of  the  equator, 
and  lowest  at  64°  north  and  about  70°  south  of  the  equa- 
tor ;  also  that  the  mean  height  of  the  barometer  is  gener- 
ally greater  north  of  the  equator  than  south  of  it.  There 
is  a  belt  of  low  pressure  at  the  equator. 

510.  The  Mean  Height  of  the  Barometer  for  Different 
Months.  —  The  mean  height  of  the  barometer  varies  some- 
what from  month  to  month  during  the  year,  being  generally 
higher  in  winter  than  in  summer.  In  many  places  the 
mean  height  in  winter  exceeds  that  of  summer  by  half  an 
inch,  while  in  other  places  the  inequality  almost  entirely 
disappears.  At  Pekin,  China,  the  mean  height  of  the 
barometer  for  January  exceeds  that  for  July  by  three 
quarters  of  an  inch.  Throughout  a  considerable  portion 
of  the  continent  of  Asia  the  winter  mean  is  considerably 
above  that  for  the  summer.  In  the  middle  latitudes  of 
Europe  and  America  the  mean 
height  of  the  barometer  is  usually 
about  the  same  for  each  month 
of  the  year.  At  Boston  the 
mean  pressure  does  not  differ 
more  than  one  tenth  of  an  inch 
for  any  two  months  of  the  year. 
The  same  is  true  of  London  and 
Paris.  The  four  curves  B,  Z,  If, 
and  P  (Figure  466)  show  the 
monthly  fluctuations  of  the  mean 


Fig.  466. 


JFMAMJJA80NDJ 


NATURAL   PHILOSOPHY. 


433 


pressure  at  Boston,  London,  Havana,  and  Pekin.  The 
spaces  and  letters  at  the  bottom  of  the  line  represent  the 
months,  and  the  vertical  lines  the  height. 

511.  Hourly  Fluctuation  of  the  Barometer.  —  When  the 
indications  of  the  barometer  for  each  hour  of  the  day  for 
a  long  period   are   averaged,  it   will  be  found  that  these 
averages  are  not  equal  to  each  other.     The  height  of  the 
barometer   is   greatest   about    TO  A.M.   and   least   at   about 
4  P.M.     There  are  also   smaller   fluctuations  at  night,  the 
barometer  attaining  a  second  maximum  at  about  10  P.M., 
and  a  second  minimum  at  about  4  A.M.     This  diurnal  oscil- 
lation is  greatest  at  the  equator,  and  decreases  as  we  ap- 
proach either  pole. 

At  the  equator  it  is  0.104  inch;  in  latitude  40°  it  is  0.05 
inch  •  and  in  latitude  70°  it  is  only  0.003  inch.  The  three 
curves  of  Figure  467  show  the  Fig.  467. 

hourly  variation  of  pressure  at 
the  equator,  £,  at  Philadelphia, 
P,   and   at  St.   Petersburg,  S. 
The   numbers   at   the    bottom  * 
indicate  the  hours  of  the  day. 

512.  Fluctuation      depending 
on  the  Position  of  the  Moon.  — 

There  is  a  small  fluctuation  of  the  barometer  depending 
on  the  position  of  the  moon,  but  this  variation  is  exceed- 
ingly minute  and  can  be  detected  only  by  taking  the  mean 
of  the  most  accurate  observations  continued  for  a  long 
time.  These  fluctuations  indicate  a  feeble  tide  in  the 
atmosphere  similar  to  those  of  the  ocean. 

513.  Irregular  Fluctuations.  —  The  irregular  fluctuations 
of  the  barometer  are  far  greater  than  the  periodic  ones. 
In  the  middle  latitudes  the  barometer  is  almost  constantly 
in  motion,  and  these  fluctuations  are  so  great  and  so  irreg- 
ular as  in  great  measure  to  conceal  the  periodic  movement. 
Jt  is  only  by  taking  the  mean  of  a  long  series  of  observa- 


\ 


J 


434  NATURAL   PHILOSOPHY. 

tions  that  the  latter  can  be  detected  at  all.  The  difference 
between  the  greatest  and  least  heights  of  the  barometer 
for  a  single  month  is  called  the  monthly  oscillation,  and  by 
combining  observations  extending  over  a  series  of  years 
we  obtain  the  mean  monthly  oscillation.  The  mean  monthly 
oscillation  is  least  at  the  equator,  and  increases  as  we  pro- 
ceed towards  the  poles. 

At  the  equator  it  is  about  -fa  of  an  inch  ;  in  latitude  30° 
it  is  T%of  an  inch  ;  in  latitude  45°,  over  the  Atlantic  Ocean, 
it  is  i  inch;  in  latitude  65°  it  is  ij  inches.  During  the 
three  winter  months  the  mean  monthly  oscillation  is  about 
3  greater  than  the  numbers  given  above.  These  oscilla- 
tions are  generally  less  over  the  continents  of  Europe  and 
America  than  over  the  Atlantic  Ocean  on  the  same  parallel. 
The  extreme  fluctuations  of  the  barometer  are  much  greater 
than  the  mean  monthly  oscillations.  The  greatest  and 
least  observed  heights  of  the  barometer  at  Boston  are 
31.125  inches  and  28.47  inches,  the  difference  being  2.655 
inches.  The  greatest  observed  difference  at  London  is 
3  inches;  and  at  St.  Petersburg,  3.5  inches. 

II. 
TEMPERATURE  OF  THE  ATMOSPHERE. 

514.  How  the  Atmosphere  becomes  Heated.  —  The  atmos- 
phere becomes  heated  partly  by  absorbing  the  direct  rays 
of  the  sun,  partly  by  contact  with  the  wanner  earth,  and 
partly  by  absorbing  the  obscure  heat  radiated  from  the 
earth. 

A  portion  of  the  heat  emitted  by  the  sun  is  absorbed  by 
our  atmosphere  before  it  can  reach  the  earth's  surface.  It 
is  estimated  that  on  a  clear  day  our  atmosphere  absorbs 
about  one  fourth  of  the  rays  which  traverse  it  vertically. 
The  heat  thus  absorbed  raises  the  temperature  of  the 


NATURAL    PHILOSOPHY. 


435 


atmosphere.  It  is  mainly  the  obscure  rays  that  are  ab- 
sorbed by  the  atmosphere,  and  this  absorption  is  done 
chiefly  by  the  watery  vapor  in  the  atmosphere.  The  rays 
of  the  sun  which  reach  the  earth's  surface  are  absorbed  by 
it.  The  surface  thus  becomes  heated,  and  communicates 
heat  to  the  air  which  rests  upon  it.  This  heated  air,  be- 
coming lighter  through  expansion,  rises  and  gives  place  to 
colder  air  from  above,  which  in  turn  becomes  heated  by 
contact  with  the  earth. 

As  the  surface  of  the  earth  becomes  warmed  by  the 
direct  rays  of  the  sun,  it  radiates  obscure  heat  back  into 
the  atmosphere.  These  rays  are  partially  absorbed  by  the 
atmosphere,  especially  in  the  lower  layers,  where  watery 
vapor  is  most  abundant. 

Fig.  468. 


12    2      4     G      8     10     n 

515.  Hourly  Variations  of  Temperature.  —  The  tempera- 
ture of  a  place  varies  from  hour  to  hour  according  to  the 
elevation  of  the  sun  above  the  horizon.  The  average  of 
observations  taken  for  a  long  period  shows  that  the  mean 
hourly  variations  of  temperature  are  extremely  regular. 
The  curve  in  Figure  468  shows  the  mean  hourly  variations 
of  temperature  at  New  Haven.  There  is  a  maximum  and 
minimum  of  temperature  each  day,  the  minimum  occurring 
about  an  hour  before  sunrise,  and  the  maximum  about  two 
hours  after  noon. 

The  highest  temperature  of  the  day,  other  things  being 


436 


NATURAL   PHILOSOPHY. 


equal,  occurs  when  the  amount  of  heat  lost  each  instant 
by  radiation  is  just  equal  to  that  received  from  the  sun. 
Before  midday  the  earth  receives  more  heat  from  the  sun 
than  it  loses  by  radiation,  and  the  temperature  rises.  After 
noon  the  earth  receives,  each  instant,  less  heat  from  the 
sun  than  it  did  at  noon  ;  but  for  some  time  it  still  receives 
heat  faster  than  it  parts  with  it.  Hence  the  maximum  of 
temperature  occurs  some  time  after  noon.  During  the 
night  we  receive  no  direct  heat  from  the  sun,  and  the  earth 
cools  by  radiation.  About  an  hour  before  sunrise  the  heat 
received  from  the  returning  sun  becomes  equal  to  that  lost 
by  radiation,  and  the  temperature  ceases  to  fall. 

516.  Mean  Temperature  of  a  Day.  —  The  mean  temper- 
ature of  a  day  is  the  average  temperature  of  the  24  hours. 
This  might  be  found  by  observing  the  temperature  each 
hour  of  the  day,  and  dividing  the  sum  of  these  observed 
temperatures  by  24.     This  method  is  very  laborious.     In 
practice,  the  mean  temperature  of  the  day  is  found  by 
taking  the  average  of  three  observations,  one  at  6  A.  M.,  one 
at  2  P.  M.,  and  one  at  9  P.  M. 

517.  Monthly  Variations  of  Temperature.  —  The  curves 
of  Figure  469    show  the  mean  temperature  and  also  the 

mean  maximum  and  minimum 
temperature  for  each  month  of 
the  year  at  New  Haven,  accord- 
ing to  observations  extending 
through  86  years.  The  months 
are  given  on  the  horizontal  line 
at  the  bottom,  and  the  degrees 
of  temperature  on  the  vertical 
line  at  the  left.  The  warmest 
months  of  the  year  for  this  place 

are  July  and  August,  the  maximum  occurring  about  the 
24th  July.  The  coldest  month  is  January,  the  minimum 
occurring  about  the  2ist  of  this  month.  The  difference 


Fig.  469. 


NATURAL    PHILOSOPHY.  437 

between  the  maximum  and  minimum  temperature  is  greater 
for  the  cold  than  for  the  warm  months. 

The  chief  reasons  why  it  is  colder  during  the  winter 
months  than  during  the  summer  months  are  that  the  sun 
is  farther  from  the  zenith  and  is  a  shorter  time  above  the 
horizon. 

The  earth  is  receiving  the  most  heat  from  the  sun  at  the 
time  of  the  summer  solstice,  but  the  temperature  continues 
to  rise  as  long  as  the  earth  receives  more  heat  from  the 
sun  during  the  day  than  it  loses  by  radiation  during  the 
night.  During  the  autumn  the  loss  at  night  is  much  greater 
than  the  gain  by  day,  and  the  temperature  rapidly  falls. 
The  temperature  continues  to  fall  till  the  gain  by  day  is 
again  equal  to  the  loss  by  night.  This  does  not  occur  till 
some  time  after  the  winter  solstice. 

518.  Irregular  Fluctuations   of    Temperature.  —  Besides 
the  periodic  variations  of  temperature,  there  are  constant 
irregular  fluctuations  of  temperature.     These  are  liable  to 
occur  any  hour  of  the  day  and  any  day  of  the  year. 

519.  Variations  of  Temperature  with  the  Latitude.  —  As 
we  proceed  from  the  equator  to  the  poles,  the  temperature 
generally  falls,  but  not  at  a  uniform  rate,  and  the  rate  of 
fall  will  be  different  on  different  meridians.     Hence  the 
lines  of  equal  temperature  on  the  surface  of  the  earth  do 
not  coincide  with  the  parallels  of  latitude.     Lines  which 
connect   places   of    equal   mean   temperature   are    called 
isothermal  lines.     The  isothermal  lines  for  every  ten  de- 
grees are  shown  on  the  accompanying  map  (Figure  470). 
These  lines  show  the  general  distribution  of  heat  over  the 
surface  of  the  earth.     They  are  seen  to  be  much  more 
irregular  on  and  around  the  continents  than  in  the  oceans. 

520.  The  Temperature  of  the  two  Sides  of  the  Atlantic.  — 
It  will  be  seen  from  the  map  in  Figure  470  that  the  mean 
temperature  of  the  eastern  side  of  the  Northern  Atlantic 
Ocean  is  considerably  higher  than  that  of  the  western  side 


NATURAL   PHILOSOPHY. 


N  \  I  t   RAL    PHILOSOPHY. 


439 


at  the  same  latitude.  The  temperature  of  Dublin  is  as 
high  as  that  of  New  York,  though  the  former  is  13°  farther 
north,  while  near  Lake  Superior,  in  latitude  50°,  we  find 
the  same  mean  temperature  as  at  the  North  Cape,  in 
latitude  72°. 

The  high  temperature  of  the  European  coast  is  due  to 
the  high  temperature  of  the  Northern  Atlantic  and  the 
prevalent  westerly  winds.  The  Gulf  Stream  conveys  the 
warm  water  of  the  equatorial  region  into  the  North  Atlan- 
tic. The  temperature  of  the  North  Atlantic  is  thus  raised 
considerably  above  what  is  due  to  its  latitude,  and  the 
prevalent  westerly  winds  of  the  middle  latitudes  carry  this 
heat  to  the  eastern  side  of  the  Atlantic  and  away  from  its 
western  side. 

521.  The  Temperature  of  the  two  Sides  of  the  Pacific.  — 
Owing  to  the  currents  of  the   Pacific  Ocean,  there  is  a 
corresponding  *difference  of  temperature  between  its  east- 
ern and  western  coast,  the  temperature  of  the  east  coast 
being  higher  than  that  of  the  west.     This  causes  a  marked 
difference  of  temperature  between  the  eastern  and  western 
coasts  of  North  America  at  places  on  the  same  parallel. 
The  same  isothermal  line  will  be  found  10  or  15  degrees 
farther  north  "on  the  Pacific  coast  of  North  America  than 
on  the  Atlantic  coast. 

522.  The   Temperature  of  the   Northern    and    Southern 
Hemispheres.  —  The   mean   temperature    of   the   northern 
hemisphere  is  nearly  three  degrees  higher  than   that  of 
the  southern  hemisphere. 

The-  unequal  temperature  of  the  two  hemispheres  is 
probably  due  to  the  unequal  distribution  of  land  and 
water.  The  northern  hemisphere  contains  more  land 
and  less  water  than  the  southern.  In  the  southern  hemi- 
sphere the  sun's  rays  fall  chiefly  upon  water,  and  a  large 
amount  of  heat  is  consumed  in  the  evaporation  of  water. 
In  the  condensation  of  vapor  the  heat  is  again  liberated. 


44°  NATURAL   PHILOSOPHY. 

Observations  show  that  there  is  more  condensation  in  the 
northern  hemisphere  than  in  the  southern.  Thus  the 
southern  hemisphere  is  cooled  more  by  evaporation  and 
warmed  less  by  condensation  than  the  northern  hemi- 
sphere. 

523.  Mean  and  Extreme  Temperatures  of  a  Place.  —  Two 
places  having  the  same  mean  temperature  may  differ  greatly 
in  their  extreme  temperatures.    'New  York  and  Liverpool 
have  the  same  mean  temperature,  but  the  difference  be- 
tween the  mean  temperature  of  the  three  summer  months 
and  that  of  the  three  winter  months  is  twice  as  great  in 
New  York  as  in  Liverpool. 

In  some  localities  the  mean  temperature  of  the  hottest 
month  of  the  year  is  less  than  5°  above  that  of  the  coldest, 
while  in  other  localities  it  is  70°  or  80°  above. 

524.  Marine  and  Continental  Climates.  —  The  tempera- 
ture of  water  changes  less  than  that  of  land.     The  specific 
heat  of  water  being  much  higher  than  that  of  land,  a  much 
greater  amount  of  heat  is  consumed  in  raising  the  tem- 
perature of  an  equal  mass  of  water  the  same  number  of 
degrees,  and  a  much  greater  amount  of  heat  is  liberated 
in  the  cooling  of  an  equal  mass  of  water.     Hence  when 
land  and  water  are  receiving  or  losing  heat  at  the  same 
rate,  the   temperature   of  the  former  will  rise   higher  or 
fall  lower  than  that  of  the  latter  in  the  same  time.     The 
high  latent  heat  of  watery  vapor  tends  to  keep  the  tem- 
perature of  water  uniform,  a  large  amount  of  heat  being 
rendered  latent  by  evaporation  when  the  temperature  is 
rising,  and   an   equally  large   amount  being  liberated   by 
condensation  when  the  temperature  is  falling.     Again,  the 
sun's  rays  penetrate  water  to  a  greater  depth  than  land, 
and  at  the  same  time  the  currents  in   the  ocean  tend  to 
equalize  the  temperature  of  the  water  at  different  depths. 
Hence  while   land    becomes  heated  only  at  the  surface, 
water  becomes  heated  to  a  considerable  depth  below  the 


NATURAL    PHILOSOPHY.  441 

surface.  The  greater  depth  of  water  heated  and  cooled  as 
the  temperature  rises  and  falls  would  cause  the  tempera- 
ture to  change  less  at  the  surface  of  water  than  of  land. 

When  the  temperature  of  a  place  is  controlled  mainly  by 
the  ocean,  the  temperature  is  equable,  and  the  climate  is 
called  marine;  when,  on  the  contrary,  it  is  controlled 
mainly  by  the  continent,  the  temperature  is  extreme,  and 
the  climate  is  called  continental.  On  the  eastern  coast  of 
the  United  States,  where  the  prevalent  winds  are  from  the 
land,  there  is  a  great  annual  range  of  temperature  and  a 
continental  climate ;  while  in  the  western  part  of  Europe, 
where  the  prevalent  winds  are  from  the  ocean,  the  tem- 
perature is  more  uniform  and  the  climate  marine. 

525.  Change  of  Temperature   with  the   Elevation. —  As 
we  ascend  in  the  atmosphere  from  the  earth,  the  tempera- 
ture falls.     The  rate  of  decrease  varies  with  the  latitude 
of  the  place,  with  the  time  of  the  year,  and  with  the  hour 
of  the  day.     It  is  more  rapid  in  warm  countries  than  in 
cold,   and   in   the   hot   months  than  in   the   cold.     It   is 
most  rapid  about  5  P.  M.,  and  least  rapid  about  sunrise. 
The  change  is  also  most  rapid  near  the  earth,  and  decreases 
as  we  ascend. 

There  are  two  main  reasons  why  the  temperature  of  the 
atmosphere  falls  as  we  ascend  :  (i)  The  air  of  the  earth's 
surface  becomes  heated  and  expanded,  and  tends  to  rise 
because  of  its  diminished  specific  gravity.  As  the  air 
ascends  it  meets  with  less  pressure,  and  therefore  expands  ; 
this  expansion  consumes  heat,  and  causes  the  temperature 
to  fall.  (2)  The  moisture  in  the  air  becomes  less  and 
less  as  we  ascend,  and  hence  there  is  less  absorption  of 
the  solar  rays,  and  it  is  only  the  rays  which  are  absorbed 
that  tend  to  raise  the  temperature  ;  also  there  will  be  less 
hindrance  to  the  escape  into  space  of  the  heat  radiated  from 
the  atmosphere. 

526.  The  Line  of  Perpetual  Snoiv.  —  Since  the  tempera- 


442  NATURAL    PHILOSOPHY. 

ture  of  the  atmosphere  falls  as  we  ascend,  the  tops  of  high 
mountains,  even  within  the  tropics,  are  covered  with  per- 
petual snow.  The  snow-line  depends  more  upon  the 
temperature  of  the  hottest  month  than  upon  the  mean  tem- 
perature of  the  year.  It  is  not  therefore  the  line  whose 
mean  temperature  is  32°.  It  depends  also  to  a  consider- 
able extent  upon  the  annual  snow-fall. 

Under  the  equator  the  height  of  the  snow-line  varies 
from  15,000  to  16,000  feet,  where  the  mean  annual  temper- 
ature is  35°.  On  the  Alps  the  average  height  of  the  snow- 
line  is  8800  feet,  where  the  mean  annual  temperature  is 
25°  ;  while  on  the  coast  of  Norway  its  height  is  only  2400 
feet,  where  the  mean  annual  temperature  is  21°. 

527.  The  Atmosphere  a  Regulator  of  Temperature. — 
During  the  day  the  atmosphere  absorbs  a  portion  of  the 
sun's  rays,  so  that  they  are  less  excessive  on  reaching  the 
earth.  A  considerable  portion  of  the  heat  thus  absorbed 
during  the  day  is  rendered  latent  by  expansion.  At  night 
the  air  intercepts  a  part  of  the  rays  emitted  by  the  earth, 
and  so  keeps  the  heat  from  escaping  into  space.  At  the 
same  time,  as  the  air  is  cooled,  it  contracts,  and  so  liberates 
the  heat  that  was  rendered  latent  by  expansion  during  the 
day.  Were  it  not  for  the  atmosphere  the  days  would  be 
very  much  hotter  and  the  nights  very  much  colder  than 
they  are  now.  It  is  chiefly  by  means  of  the  watery  vapor 
present  in  the  atmosphere  that  it  acts  thus  as  a  regulator 
of  temperature. 


III. 
HUMIDITY  OF  THE   ATMOSPHERE. 

528.  The  Hygrometer.  —  An  instrument  capable  of  meas- 
uring the  moisture  of  the  air  is  called  a  hygrometer.  A 
hygroscope  is  an  instrument  which  merely  shows  that  there 


NATURAL    PHILOSOPHY. 


443 


Fig.  471. 


are  changes  of  moisture,  without  being  capable  of  measur- 
ing the  amount  of  moisture  present.  The  hygrometer 
shown  in  Figure  471  is  one  of 
the  most  convenient  and  ac- 
curate in  use.  It  is  known 
as  Mason's  hygrometer.  It 
consists  of  two  thermometers. 
The  bulb  of  one  of  these  is 
kept  moist  by  being  covered 
with  muslin  or  silk,  the  fibres 
of  which  dip  into  a  reservoir 
of  water.  The  water  is  drawn 
up  to  the  bulb  by  capillary 
action,  and  the  evaporation 
from  its  surface  lowers  its 
temperature.  Hence  the  wet- 
bulb  thermometer  will  always 
show  the  lower  temperature. 
The  greater  the  difference  of 
reading  between  the  two  ther- 
mometers, the  faster  the  evapo- 
ration from  the  wet  bulb  and 
the  drier  the  air. 

529.  Humidity  of  the  Air.  —  The  amount  of  moisture 
which  a  cubic  foot  of  air  can  hold  increases  with  the  tem- 
perature.    When  the  air  contains  all  the  moisture  it  can 
hold  at  that  temperature,  it  is  said  to  be  saturated  with 
moisture.     By  the  humidity  of  the  air  we  do  not  mean  the 
absolute  amount  of  moisture  in  it,  but  its  degree  of  satura- 
tion.    If  the  air  is  half  saturated,  its  humidity  is  50  ;  if 
three-quarters  saturated,  75  ;  etc. 

530.  Dew-Point.  —  The  dew-point  is  the  temperature  at 
which  the  air  would  become  saturated  with  the  moisture  in 
it,  and  its  moisture  begin  to  be  deposited  as  dew.     It  is 
not  a  fixed  temperature,  like  those  of  the  freezing  and  boil- 


444 


NATURAL    PHILOSOPHY. 


ing  points,  but  varies  with  the  temperature  and  humidity 
of  the  air.  The  greater  the  humidity  of  the  air,  the  less  the 
temperature  would  have  to  fall  to  reach  the  dew-point. 

From  the  reading  of  the  two  thermometers  in  Mason's 
hygrometer,  it  is  possible  to  calculate  the  temperature  of 
the  dew-point,  the  humidity  of  the  air,  and  the  number  of 
grains  of  moisture  in  a  cubic  foot  of  air.  Tables  are  pre- 
pared to  be  used  with  this  instrument  in  which  the  results 
of  these  calculations  are  given  for  different  readings  of  the 
thermometers. 

The  difference  between  the  temperature  of  the  dew- 
point  and  that  of  the  air  is  called  the  complement  of  the 
dew-point.  The  drier  the  air,  the  greater  the  complement 
of  the  dew-point. 

In  ordinary  pleasant  weather  the  complement  of  the  dew- 
point  is  from  10°  to  15°.  Occasionally,  at  Philadelphia,  it 
amounts  to  25°  or  30°,  and  has  been  observed  as  high  as  45°. 
In  India  it  has  been  known  to  reach  61°,  and  in  California  78°. 
In  the  last  case  the  atmosphere  would  contain  only  6  per  cent 
of  the  vapor  required  for  its  saturation. 

531.  Diurnal  Variation  in  the  Vapor  present  in  the 
Atmosphere.  —  The  amount  of  vapor  present  in  the  atmos- 
phere is  subject  to  great  fluctuations,  some  of  which  are 
irregular  and  others  periodic.  As  a  rule,  the  amount  of 
vapor  in  the  atmosphere  is  least  about  an  hour  before 
sunrise,  and  greatest  just  before  sunset,  the  mean  diurnal 
variation  amounting  to  about  ^  of  the  average  amount 
of  vapor  present. 

The  curve  in  Figure  472  shows  the  diurnal  variation  at 
Fig.  472  Philadelphia,  the  figures  at 

the  left  indicating  the  pres- 
sure of  the  vapor  in  inches 
of  mercury,  at  the  hours 
given  at  the  bottom.  This 
diurnal  variation  in  the  amount  of  vapor  is  due  to  the 


NATURAL    PHILOSOPHY.  445 

diurnal  change  in  temperature.  As  the  temperature  rises 
during  the  day,  more  water  is  evaporated  from  the  ocean 
and  the  moist  earth,  and  the  amount  of  vapor  in  the  air 
increases.  During  the  night  a  portion  of  the  vapor  is  con- 
densed in  the  form  of  dew  and  hoar-frost,  and  the  amount 
of  vapor  present  in  the  air  decreases. 

532.  Annual  Variation  in  the  Amount  of  Vapor  present 
in  the  Atmosphere.  —  In  the  northern  hemisphere  the  mean 
amount  of  vapor  present  in  the  atmosphere  is  greatest  in 
July,   when   the  mean  temperature   is  highest,  and   least 
in  January,  when  the  mean  temperature  is  lowest.     This 
is  due  to  the  more  rapid  evaporation  in  summer  than  in 
winter. 

533.  Variation  in  the  Amount  of  Vapor  with  the  Elei>a- 
tion.  —  The   humidity  of   the   atmosphere  as   a   rule   de- 
creases as  we  rise  above  the  earth,  though  there  is  a  slight 
increase  of  humidity  for  the  first  3000  feet.    At  the  highest 
elevations  at  which  observations  have  been  taken  the  air 
has  never  been  found  entirely  free  from  moisture. 

534.  Diurnal  Variation  of  the  Pressure  of  the  Gaseous 
Atmosphere.  —  The  earth  is  really  enveloped  in  two  atmos- 
pheres, one  of  vapor  and  one  of  permanent  gases.     These 
two  atmospheres  are  mixed  together,  and  by  their  com- 
bined pressure  cause   the  rise  of  the  barometer.     Other 
things  being  equal,  the  greater  the  amount  of  vapor  pres- 
ent in  the  atmosphere  the  higher  the  barometer,  and  vice 
versa.     Fluctuations  in  the  height  of  the  barometer   are 
caused  by  changes  in  the  temperature  of  the  air  and  the 
amount  of  vapor  present  in  the  atmosphere.     A  diminution 
of  vapor  and  an  increase  in  temperature  both  tend  to  cause 
the  barometer  to  fall. 

If  we  subtract  the  pressure  of  the  vapor  in  the  atmos- 
phere from  that  of  the  whole  atmosphere,  the  remainder 
will  be  the  pressure  of  the  gaseous  atmosphere.  When 
this  deduction  from  the  total  pressure  has  been  made,  it  is 


446 


NATURAL    PHILOSOPHY. 


Fig.  473- 


found  that  at  Philadelphia  the  pressure  of  the  gaseous 
atmosphere  is  greatest  at  about  an  hour  after  sunrise  and 
least  about  4  p.  M.,  as  is 
shown  by  the  curve  of  Fig- 
ure 473. 

This  fluctuation  of  the 
pressure  of  the  gaseous  at- 
mosphere is  evidently  due 
to  the  variation  of  solar  heat  As  the  heat  of  the  day  in- 
creases, the  atmosphere  becomes  warmed,  expands,  and 
swells  up  to  a  height  greater  than  it  had  at  night.  The 
upper  portion  therefore  flows  off  laterally  in  all  directions  to 
places  where  the  height  of  the  atmosphere  is  less,  owing  to 
a  lower  temperature.  This  overflow  diminishes  the  amount 
and  pressure  of  the  air  at  the  place  from  which  it  takes 
place,  and  increases  the  amount  and  pressure  of  the  air  at 
the  place  towards  which  the  overflow  proceeds.  The  outflow 
increases  with  the  temperature,  and  continues  awhile  after 
the  hottest  part  of  the  day  is  passed.  Hence  the  pressure 
continues  to  decrease  for  some  time  after  the  hottest  part 
of  the  day.  As  the  temperature  falls  at  night,  the  air 
again  contracts,  and  its  depth  becomes  less  than  during 
the  day,  and  the  depression  thus  produced  gives  rise  to  an 
inflow,  which  increases  the  amount  and  pressure  of  the  air. 
This  inflow  of  air  and  increase  of  pressure  continue  for 
some  time  after  the  coldest  part  of  the  day  is  past. 

The  pressure  of  the  vapor  and  that  of  the  gaseous 
atmosphere  have  each  but  one  maximum  and  minimum 
a  day.  Their  maxima  and  mimima  do  not,  however, 
coincide,  but  occur  at  nearly  opposite  hours  in  the  day. 
The  combination  of  these  two  pressures  gives  two  maxima 
and  two  minima  in  the  resulting  pressures. 

535.  Annual  Variation  of  the  Pressure  of  the  Gaseous 
Atmosphere.  —  In  the  northern  hemisphere  the  pressure 
of  the  gaseous  atmosphere  is  greatest  in  January,  when  the 


NATURAL    PHILOSOPHY. 


447 


temperature  is  lowest,  and  least  in  July,  when  the  tempera- 
ture is  highest.  The  difference  between  the  summer  and 
winter  pressures  of  the  gaseous  atmosphere  is  very  unequal 
in  different  countries.  In  the  eastern  part  of  the  United 
States  this  difference  amounts  to  about  half  an  inch,  while 
in  Central  Asia  it  amounts  to  above  an  inch,  and  at  the 
equator  is  scarcely  appreciable.  Fig-  Fig.  474. 

ure   474   shows   the   annual    curve    of    Kt 
pressure  at  Pekin,   China. 

The  annual  fluctuation  in  the  pres-  |fc8 
sure  of  the  gaseous  atmosphere  is  due  *" 
to  the  annual  variation  in  temperature,  zo.o 
and  the  amount  of  the  fluctuation  in-  * 
creases  with  the  annual  range  of  temperature.  During  the 
summer  the  air  expands  and  overflows,  and  the  pressure 
falls.  During  the  winter  the  contraction  of  the  air  gives 
rise  to  an  inflow  and  an  increase  of  pressure. 

In  the  temperate  zones  of  Europe  and  America  the 
increase  in  the  amount  of  vapor  in  the  atmosphere  nearly 
balances  the  loss  of  weight  sustained  by  the  gaseous 
atmosphere,  so  that  the  pressure  of  the  whole  atmosphere 
remains  about  the  same  throughout  the  year. 


MOVEMENTS    OF   THE   ATMOSPHERE. 

536.  Winds.  —  Wind  is  air  in  motion.  Although  the 
winds  are  proverbially  variable  and  fickle,  they  are  gov- 
erned by  laws  as  fixed  and  definite  as  those  which  regulate 
the  temperature  and  pressure  of  the  atmosphere. 

The  force  of  a  wind  may  be  indicated  either  by  its 
velocity  in  miles  per  hour  or  by  its  pressure  in  pounds  per 
square  foot.  The  character,  velocity,  and  pressure  of 
various  winds  are  given  in  the  following  table,  taken  from 
Loomis  :  — 


448 


NATURAL    PHILOSOPHY. 


Character. 

Velocity 
in  Miles 
per 
Hour. 

Force  in 
Pounds 
per  Square 
Foot. 

Gently  pleasant  
Pleasant  brisk  

4 

O.o8 

Very  brisk  
High  wind  

25 

3.00 
6 

Very  high  wind  
Strong  gale  

45 
60 

10 
18 

Violent  gale  
Hurricane  ....  
Most  violent  hurricane  

70 
80 

IOO 

24 
3i 
49 

From  a  long  series  of  observations  at  Philadelphia  it 
appears  that  the  mean  velocity  of  the  wind  is  1 1  miles  an 
hour.  The  mean  velocity  varies  somewhat  during  the 
day  and  during  the  year.  It  is  least  about  sunrise  and 
greatest  about  2  P.  M.  It  is  nearly  uniform  during  the 

Fig.  475- 


, 

/ 

\ 

\ 

/ 

X, 

19.    ' 

-" 

>  r. 

night.  The  curve  in  Figure  475  shows  this  diurnal  varia- 
tion in  the  force  of  the  wind,  the  figures  in  the  vertical 
line  indicating  the  pressure  of  the  wind  in  pounds  per 
square  foot. 

According  to  the  observations  at  Philadelphia,  the  mean 
velocity  of  the  wind  is  9  miles  per  hour  in  summer  and  14 
miles  in  winter.  The  mean  velocity  varies  somewhat  in 
different  parts  of  the  globe,  but  within  rather  narrow 


NATURAL    PHILOSOPHY.  449 

limits.     The  mean  velocity  at  sea  appears  to  be  about  18 
miles  per  hour. 

537.  Cause  of  Winds.  —  Movements  of  the  atmosphere 
are  produced  either  by  the  unequal  pressure  of  the  atmos- 
phere at  different  points,  or  by  the  unequal  specific  gravity 
of  different  portions  of  the  atmosphere. 

Surface  currents  will  always  set  \\\from  a  region  of  high 
pressure  towards  a  region  of  low  pressure. 

Unequal  specific  gravity  of  the  air  may  be  due  to 
inequalities  of  temperature  or  of  humidity.  Suppose 
the  surface  of  the  earth  in  Fig 
the  neighborhood  of  C  (Fig- 
ure 476)  to  become  exces- 
sively heated.  The  air  above 
C  will  by  expansion  become 
lighter  than  the  surrounding 
air.  This  lighter  air  will  ac- 
cordingly rise,  and  its  place 
will  be  supplied  by  an  inflow 
along  the  surface  from  every 
side.  At  the  same  time  the  heated  column,  rising  above 
the  surrounding  atmosphere,  gives  rise  to  an  outflow  at  the 
top.  At  a  certain  dis-  Fig.  477- 
tance  from  the  heated  ^ -^  ^ ^ 

descending  currents  to     j  | 


ted     4~~ ^t 

be    I  | 


column    there    will 

supply  the  place  of  the    |  1 

air  which  is  flowing  in     ^ 

towards  the  heated  region  at  the  surface  of  the  earth. 

The  system  of  currents  that  would  be  developed  on 
every  side  of  an  excessively  heated  region  is  shown  in 
Figure  477,  the  arrows  indicating  the  direction  of  I 
currents.  A  system  of  currents  in  just  the  opposite  direc- 
tion would  be  developed  on  every  side  of  an  excessively 
cold  region. 


450  NATURAL    PHILOSOPHY. 

The  specific  gravity  of  the  vapor  of  water  is  only  about 
two  thirds  that  of  dry  air.  As  it  takes  time  for  the 
vapor  to  diffuse  itself  into  the  atmosphere,  an  excess 
of  aqueous  vapor  tends  to  produce  a  region  of  low  spe- 
cific gravity,  and  so  to  develop  a  system  of  currents 
similar  to  those  developed  by  a  region  of  high  tempera- 
ture. 

Were  the  barometer  everywhere  to  indicate  the  same 
pressure  at  the  surface  of  the  earth,  the  wind  at  the  surface 
would  still  \Aovtfrom  a  region  of  low  temperature  to  a  re- 
gion of  high  temperature,  wcAfrom  a  region  of  little  vapor 
to  a  region  of  excessive  vapor. 

538.  The  Direction  of  the  Winds  modified  by  the  Rotation 
of  the  Earth.  —  The  earth's  rotation  from  west  to  east  in 
24  hours  is  on  an  axis  perpendicular  to  its  equator.  Every 
point  on  the  earth's  surface  is  carried  around  in  the  same 
time,  but  points  near  the  equator  describe  longer  paths,  and 
hence  must  move  with  greater  velocity  than  those  near  the 
poles.  The  velocity  of  rotation  at  the  surface  is  greatest 
at  the  equator  and  decreases  towards  the  poles.  At  the 
equator  it  is  1036  miles  per  hour;  15°  from  the  equator  it 
is  1000  miles  per  hour ;  30°  from  the  equator,  897  miles  ; 
45°  from  the  equator,  732  miles  ;  60°  from  the  equator, 
518  miles;  75°  from  the  equator,  268  miles. 

If  a  mass  of  quiescent  air  from  parallel  30°  were  sud- 
denly transported  to  parallel  15°,  it  would  have  an  easterly 
motion  of  103  miles  an  hour  less  than  that  of  the  parallel 
arrived  at.  It  would  therefore  seem  to  be  moving  over 
the  surface  of  the  earth  westward  at  the  rate  of  103  miles 
an  hour.  Of  course  it  would  really  be  the  surface  of  the 
earth  which  would  be  moving  under  it  eastward  at  that 
rate.  The  effect  upon  bodies  on  the  surface  of  the 
earth  would  be  the  same  as  if  the  earth  was  stationary, 
and  the  wind  blowing  over  it  to  the  west  at  the  above 
rate. 


NATURAL   PHILOSOPHY.  451 

If,  on  the  other  hand,  a  mass  of  quiescent  air  were  sud- 
denly transported  from  parallel  15°  to  parallel  30°,  it  would 
have  an  easterly  motion  of  103  miles  an  hour  greater  than 
the  parallel  arrived  at. 

In  general,  any  wind  blowing  towards  the  equator  is 
deflected  towards  the  west  by  the  rotation  of  the  earth,  so 
as  to  make  it  an  easterly  wind ;  and  any  wind  blowing/raw 
the  equator  is  deflected  towards  the  east  by  the  rotation  of 
the  earth,  so  as  to  make  it  a  westerly  wind. 

The  rotation  of  the  earth  deflects  every  wind  north  of 
the  equator  towards  the  right  of  an  observer  looking  in  the 
direction  towards  which  the  wind  blows ;  and  every  wind 
south  of  the  equator,  towards  his  left. 

539.  System  of  Winds.  —  There  are  three  great  systems 
of   winds  upon   the   globe,  namely,   the   trade-winds,   the 
middle- latitude  winds,  and  the  polar  winds. 

540.  Trade- Winds. — There    is   a    belt   of    excessively 
heated  air  surrounding  the  earth  within  the  tropics.     This 
heated  air  develops  a  system  of  currents  on  each  side  of 
it,  similar  to  those  described  in  section  537.     Surface  cur- 
rents set  in  towards  the  equator  from  the  north  and  the 
south,  and  upper  currents  from  the  equator  towards  the 
north  and  the  south.     The  rotation  of  the  earth  deflects 
the  surface  currents  towards  the  west,  so  as  to  make  them 
easterly  winds  ;  and  the  upper  currents  towards  the  east, 
so  as  to  make  them  westerly  winds.     The  trade-wind  north 
of  the  equator  is  a  northeast  wind,  and  that  south  of  the 
equator  is  a  southeast  wind. 

In  the  Atlantic  Ocean  the  northeast  trades  extend  on  an 
average  from  about  7°  north  of  the  equator  to  about  29°  f  while 
the  southeast  trades  extend  about  20°  south  of  the  equator. 
Between  these  two  trades  there  is  a  belt  of  calms  or  variable 
winds,  varying  at  different  seasons  from  150  to  500  miles  in 
breadth.  The  centre  of  this  belt  is  about  5°  north  of  the 
equator. 


452  NATURAL    PHILOSOPHY. 

The  trades,  with  their  intervening  belt  of  calms,  move  north- 
ward in  summer  and  southward  in  winter.  In  the  spring  the 
centre  of  the  belt  of  calms  is  only  i°  or  2°  north  of  the  equator, 
while  in  summer  it  is  9°  or  10°  north  of  the  equator. 

541.  Cause  of  the  High  Barometer  near  the  Parallel  oj 
32°.  —  As  the  upper  equatorial  currents  move  towards  the 
poles  they  tend  to  increase  the  pressure  of  the  atmosphere 
towards  the  north  and  the  south  ;  for  since  the  meridians 
converge   as  we   proceed  from   the  equator   towards   the 
poles,  the  air  as  it  moves  towards  the  poles  must  increase 
in  depth,  and  so  produce  a  greater  pressure  at  the  surface. 
The  distance  between  the  meridians  is  nearly  one  sixth 
less  in  latitude  32°  than  at  the  equator.     This  increased 
pressure  of  the  air  in  middle  latitudes  arrests  the  farther 
progress  of  the  polar  current,  and  a  calm  ensues.     The 
upper  air  descends  to  the  earth's  surface,  and  joins  the 
surface  current  towards  the  equator,  where  it  again  ascends, 
and  thus  maintains  a  perpetual  circulation. 

542.  The  Middle-Latitude    Winds.  —  The  high  pressure 
near   the  parallel   of  32°   gives   rise  to   surface  currents 
from  the  equator  towards  the  poles,  in  opposition  to  the 
tendency  of  the  increasing  density  of  the  air  due  to  the 
diminution   of   the   temperature    as   we   proceed   towards 
the  poles,  and  to  upper  currents  from  the  poles  towards  the 
equator.     The  surface  currents  are  deflected  by  the  rota- 
tion of  the  earth  towards  the  east,  so  as  to  make  them 
westerly  winds  ;  and  the  upper  currents  towards  the  west, 
so  as  to  make  them  easterly  winds.     These  surface  cur- 
rents are  the  prevailing  winds  of  the  middle  latitudes.     In 
the  northern  hemisphere   they  blow  from  a  point  a  little 
south  of   west,    and  in  the  southern   hemisphere  from  a 
point  a  little  north  of  west.     Throughout  the  middle  lati- 
tudes of  the  United  States  the  average  direction  of  the 
wind  is  10°  south  of  west ;  and  the  easterly  winds  are  to 
the  westerly  as  2  to  5.     In  corresponding  latitudes  in  the 


NATURAL  PHILOSOPHY 


453 


southern  hemisphere,  the  prevalent  direction  of  the  surface 
winds  is  17°  north  of  west;  and  the  easterly  winds  are  to 
the  westerly  as  i  to  5. 

These  zones  of  westerly  winds  are  from  25°  to  30°  wide. 
The  westerly  direction  of  the  wind  is  most  decided  in  the 
centre  of  the  belt,  and  gradually  diminishes  as  we  approach 
the  limit  on  either  side. 

543.  The  Polar  Winds.  —  The  extreme  cold  of  the  polar 
region  produces  the  opposite  effect  to  that  of  the  extreme 
heat  of  the  tropics.  It  produces  great  density  of  air,  and 
develops  surface  currents  blowing  from  the  poles  towards 
the  equator,  and  upper  currents  in  the  opposite  direction. 
These  currents  are  deflected  by  the  rotation  of  the  earth, 
as  in  all  other  cases.  The  polar  and  middle-latitude  winds 
encounter  each  other  near  the  parallel  of  60°. 


The  three  systems  of  surface  winds  are  shown  in  Figure 
478,  the  arrows  indicating  the  direction  of  the  wind  in 
each  belt.  Figure  479  shows  the  complete  circulation  of 
the  atmosphere.  There  are  reasons  for  supposing  that 


454 


NATURAL  PHILOSOPHY. 


high  up  in  the  atmosphere  the  current  continues  uninter- 
ruptedly from  the  equator  to  the  poles,  as  indicated  by  the 
upper  arrows  in  Figure  480. 


Fig.  479. 


Fig.  480. 


544.  Monsoons.  —  During  the  summer  months  the  sur- 
face of  the  land  becomes  heated  to  a  higher  temperature 
than  that  of  the  surrounding  water,  while  during  winter 
it  becomes  cooled  to  a  lower  temperature.  Hence  during 
the  summer  months  there  is  a  general  tendency  to  develop 
surface  winds  from  the  oceans  to  the  continents,  and  in 
the  opposite  direction  during  the  winter  months.  This 
tendency  may  either  give  rise  to  winds  in  the  direction  in 
which  it  acts,  or  merely  modify  the  direction  and  force  of 
the  prevailing  winds. 

In  the  former  case  we  have  what  are  called  monsoons, 
that  is,  winds  which  blow  during  the  summer  months  from 
the  water  tn  Jfrf  land,  and  during  the  winter  months  from 
the  land  to  the  water.  The  most  marked  monsoons  on  the 
globe  are  those  on  the  south  coast  of  Asia,  in  the  region 


NATURAL   PHILOSOPHY.  455 

of  the  northeast  trades.  The  tendency  of  the  unequal 
iieating  of  the  continent  of  Asia  and  of  the  Indian  Ocean 
during  the  winter  months  is  to  produce  a  wind  in  the  direc- 
tion of  the  trade-wind,  and  in  the  summer  months  in  the 
opposite  direction.  The  winter  monsoon  adds  to  the  force 
of  the  trade-wind,  while  the  summer  monsoon  overbalances 
the  trade,  and  produces  a  wind  in  the  opposite  direction. 

545.  Land  and  Sea  Breezes.  —  During  the  day  the  sur- 
face of  the  land  becomes  hotter  than  that  of  the  neighbor- 
ing water,  and  at  night  cooler.  There  is,  therefore,  a 
general  tendency  for  the  wind  to  blow  from  the  water  to 
the  land  during  the  day,  and  from  the  land  to  the  water  at 
night.  When  this  tendency  is  strong  enough  to  produce 
a  wind  in  the  direction  in  which  it  acts,  we  have  what  are 
called  land  and  sea  breezes,  or  winds  blowing  from  the  sea 
during  the  heat  of  the  day,  and  from  the  land  during  the 
cool  of  the  night.  These  winds  are  strongest  on  islands 
in  tropical  regions. 


V. 

CONDENSATION    IN    THE   ATMOSPHERE. 

A.    DEW  AND  HOAR-FROST. 

546.  Origin  of  Dew.  —  All  bodies  on  the  surface  of  the 
earth  are  radiating  heat  to  the  sky,  and  when  they  thus 
part  with  heat  faster  than  they  receive  it,  their  temperature 
falls  below  that  of  the  surrounding  air.  When  the  sun  is 
above  the  horizon,  they  generally  receive  heat  faster  than 
they  part  with  it  by  radiation,  but  at  night  they  usually 
radiate  heat  faster  than  they  receive  it. 

When  the  blades  of  grass,  leaves  of  plants,  and  other 
objects  on  the  surface  of  the  earth  become  cooled  by  radi- 
ation below  the  dew-point  of  the  atmosphere,  they  con- 


456  NATURAL   PHILOSOPHY. 

dense  upon  themselves  a  portion  of  the  atmospheric 
moisture  in  the  form  of  dew.  The  greatest  amount  of  dew  is 
deposited  upon  the  substances  whose  temperature  becomes 
the  lowest.  Dew  does  not  fall  from  the  sky  like  rain,  but 
collects  upon  those  bodies  which  are  cool  enough  to  con- 
dense the  vapor  in  the  air  in  contact  with  them.  A  pitcher 
of  ice-water,  on  a  warm  summer's  day,  becomes  quickly 
covered  with  a  film  of  dew,  the  cold  surface  of  the  pitcher 
condensing  the  vapor  from  the  layer  of  air  in  contact 
with  it. 

547.  Circumstances  favorable  to  the  Formation  of  Dew. — 
Anything  which  favors  the  loss  of  heat  by  radiation  is 
favorable  to  the  formation  of  dew. 

A  cloudless  night  and  an  unobstructed  exposure  to  the 
sky  are  especially  favorable  to  the  formation  of  dew,  be- 
cause they  allow  the  heat  radiated  by  bodies  to  escape 
freely  into  space.  A  cloudy  night  or  any  artificial  cover- 
ing, however  slight,  prevents  the  formation  of  dew,  for  the 
clouds  or  coverings  reflect  back  the  heat  radiated  from 
the  earth,  and  so  keep  bodies  on  its  surface  from  cooling 
below  the  dew-point. 

A  slight  breeze  favors  the  formation  of  dew  by  renew- 
ing the  air  in  contact  with  the  surface  as  fast  as  it  deposits 
its  excess  of  vapor.  A  stiff  breeze,  however,  prevents  the 
formation  of  dew  by  allowing  no  layer  of  air  to  remain 
long  enough  in  contact  with  the  surface  of  a  body  to  be- 
come sufficiently  cooled  to  deposit  its  moisture.  There  is 
little  dew  on  windy  nights. 

A  moist  atmosphere  favors  the  formation  of  dew,  because 
the  more  moisture  in  the  air,  the  less  the  reduction  of  tem- 
perature at  which  the  deposition  of  dew  will  begin.  Good 
radiators  and  bad  conductors  receive  the  greatest  amount 
of  dew.  The  temperature  of  the  surfaces  of  such  bodies 
falls  rapidly  at  night,  because  these  surfaces  lose  heat  rap- 
idly by  radiation  and  receive  it  slowly  by  conduction  from 


NATURAL    PHILOSOPHY.  457 

their  interior  or  from  the  earth  with  which  the  bodies  are 
in  contact.  Wool,  being  a  good  radiator  and  a  poor  con- 
ductor, collects  a  large  amount  of  dew  at  night,  while  a 
plate  of  polished  metal  will  receive  scarcely  any  at  all. 

548.  Formation  of  Hoar-frost.  —  When  the  temperature 
of  the  surface  is  below  the  freezing-point,  the  moisture  of 
the  atmosphere  is  deposited  upon  it  in  the  solid  state,  as 
frost.     Hoar-frost  is  not  frozen  dew,  but  frozen  vapor,  that 
is,  vapor   deposited   in    the    solid   form   without   passing 
through  the  liquid  state. 

Since  the  leaves  of  plants  sometimes  become  cooled  by 
radiation  several  degrees  below  the  air  a  few  feet  from  them, 
it  may  happen  that  there  will  be  a  frost  when  the  ther- 
mometer indicates  a  temperature  of  several  degrees  above 
the  freezing-point.  There  is  not,  however,  likely  to  be  a 
frost  unless  the  temperature  of  the  dew-point  is  below  32°. 
The  temperature  of  the  surface  will  not  fall  much  below 
the  dew-point,  because  of  the  heat  which  is  liberated  on 
the  deposition  of  the  dew. 

549.  frost  in    Valleys.  —  There  is  often  sufficient  frost 
in  valleys  and  up  to  a  certain  height  on  the  hillsides  to 
kill  plants,  while  higher  up  there  is  no  frost  at  all.     As  the 
air  on  the  hillsides  is  cooled  by  contact  with  the  cold  sur- 
face, it  gradually  settles  into  the  valley,  becoming  cooler 
and  cooler  by  contact  with  the  surface  as  it  descends,  and 
raising  the  warmer  air  bodily  out  of  the  bottom  of  the 
valley,  just  as  a  heavy  liquid  will  raise  a  lighter  one  by 
flowing   under   it.     A   thermometer   attached   to   a   high 
tower  in  a  valley  indicates  at  night  the  same  average  tem- 
perature as  a  thermometer  on  the  hillside  on  the  same 
level. 

B.   FOG  AND  MIST. 

550.  Origin  of  fog.  —  The  watery  vapor  of  the  atmos- 
phere is  transparent,  but  when  from  any  cause  a  portion 


458  NATURAL    PHILOSOPHY. 

of  the  atmosphere  becomes  cooled  below  the  dew-point,  a 
part  of  the  vapor  becomes  condensed  into  minute  drops  of 
water  which  float  in  the  atmosphere.  The  partially  con- 
densed vapor  becomes  visible  as  a  mist  or  cloud.  When 
the  condensation  takes  place  near  the  surface  of  the  earth 
it  gives  rise  to  a  fog  or  mist. 

When  steam  rises  from  a  vessel  of  warm  water  and 
mixes  with  the  colder  air  above,  a  portion  of  the  vapor  is 
condensed  into  a  mist  which  is  often  improperly  called 
steam.  Steam  proper  is  a  gaseous  body,  while  mist  is  a 
liquid  body. 

551.  Fogs  over  Rivers.  —  At  certain  seasons  of  the  year, 
and  especially  during  the  latter  part  of  the  summer,  fogs 
form  over  rivers  and  lakes  almost  every  clear  and  still 
night.     During  the  night  the  air  over  the  land  becomes 
cooler  than  the  water  of  the  lake  or  river,  and  as  the  vapor 
rises  from  the  water  it  is  partially  condensed  by  contact 
with  the  cooler  air  from  the  land,  and  gives  rise  to  a  fog 
which  floats  upon  the  surface  of  the  water. 

From  the  summit  of  Mount  Washington,  on  a  clear  and 
quiet  morning  in  August,  one  may  trace  the  course  of  the 
Connecticut  River  by  a  long  line  of  fog,  and  discover  the 
position  of  a  multitude  of  surrounding  lakes  by  the  patches 
of  fog  which  rest  upon  them,  while  other  portions  of  the 
country  are  entirely  free  from  fog. 

Such  fogs  usually  disappear  soon  after  sunrise,  often 
rising  and  drifting  away  as  clouds.  Fogs  are  often  formed 
in  a  similar  manner  over  harbors  and  bays,  and  these  fogs 
are  frequently  drifted  inland  by  gentle  currents  of  air. 
During  the  spring  of  the  year  fogs  are  sometimes  formed 
over  rivers  where  the  water  is  colder  than  the  surrounding 
air.  In  this  case  the  moist  air  is  chilled  by  contact  with 
the  cold  water,  and  a  portion  of  its  vapor  condensed  into 
a  fog. 

552.  Fogs  on  the  Breaking  up  of  Frost.  —  Extensive  fogs 


NATURAL   PHILOSOPHY.  459 

often  occur  in  midwinter  after  a  thaw  or  a  warm  rain.  In 
this  case  warm  and  moist  currents  of  air  become  chilled 
in  passing  over  the  cold  surface  of  the  frozen  ground,  and 
a  part  of  the  moisture  is  condensed  as  a  fog.  For  a  simi- 
lar reason  icebergs  are  liable  to  be  enveloped  in  mist,  the 
ice  cooling  the  surrounding  air  sufficiently  to  condense 
a  part  of  its  moisture. 

553.  Fogs  on  the  Banks  of  Newfoundland.  —  Fogs  are 
prevalent  along  the  northern  side  of  the  Gulf  Stream,  the 
warm  and  moist  air  over  the  Gulf  Stream  being  chilled  by 
contact  with  the  colder  air  from  the  water  on  the  north. 
These   fogs   are  especially  prevalent   over  the  Banks  of 
Newfoundland.     These   fogs   occur   every  month   of   the 
year,  but  are  especially  frequent  in  the  summer,  when  the 
Banks  are  enveloped  in  fog  nearly  half  of  the  time.    These 
Banks  compel  the  cold  arctic  current  at  the  bottom  of  the 
ocean  to  come  to  the  surface,  and   the  cold  water  thus 
brought  to  the  surface  chills  the  air  laden  with  moisture 
from  the  Gulf  Stream. 

554.  Mist  on   the    Tops   of   Mountains.  —  The   tops  of 
mountains  are  liable  to  be  enveloped  in  mist.     The  moun- 
tains compel  the  warm  currents  of  air  to  rise  to  pass  over 
them.     As  these  currents  rise  they  become  chilled  par- 
tially by  expansion,  and  partially  by  contact  with  the  cold 
surface  of  the  mountains.     When  the  air  is  chilled  below 
its  dew-point,  a  mist  is  formed,  which  is  again  dissipated  as 
the  air  passes  down  into  warmer  regions  on  the  other  side 
of  the  mountains. 

555.  How  Fog  is  sustained  in  the  Air.  —  The  particles 
of  fog  are  sustained  in  the  air  in  the  same  manner  as  a 
cloud  of  dust.     The  dust  remains  for  a   long  time   sus- 
pended in  the  air,  although  each  particle  may  consist  of 
matter  two  thousand  times  as  dense  as  the  air  in  which  it 
floats.     When  the  air  is  perfectly  tranquil,  Uiese  particles 
do    indeed  fall,   but  their   descent   is    so   slow  that  their 


460  NATURAL    PHILOSOPHY. 

motion  is  perceptible  only  after  a  considerable  interval  of 
time. 

556.  Indian  Slimmer.  —  "  At  certain  seasons  of  the  year 
there  occurs  a  peculiar  phenomenon  called  a  dry  fog.     In 
the  United  States  this  frequently  occurs  in  November,  or 
the  latter  part  of  October,  and  this  period  is  commonly 
known    by  the  name  of  Indian  Summer.      It  is    charac- 
terized by  a   hazy  condition  of  the    atmosphere,  a   red- 
ness of  the  sky,  absence  of  rain,  and  a  mild  temperature. 
This    appears  to   result   from   a  dry   and    stagnant  state 
of  the  atmosphere,   during  which   the  air  becomes  rilled 
with  dust  and  smoke  arising  from  numerous  fires,  by  which 
its  transparency  is  greatly  impaired.     A  heavy  rain  washes 
out  these  impurities  and  effectually  clears  the  sky. 

"  This  phenomenon  is  not  peculiar  to  the  United  States, 
a  similar  condition  of  the  atmosphere  being  frequently 
observed  in  Central  Europe.  Moreover,  this  dry  and 
stagnant  state  of  the  atmosphere  is  not  limited  to  a  single 
season  of  the  year.  The  long  periods  of  drought  which 
frequently  prevail  in  summer  are  characterized  by  a  like 
condition  of  the  atmosphere." 

C.   CLOUDS  AND  RAIN. 

557.  Nature  and  Formation  of  Clouds.  —  A  cloud  differs 
from  a  fog  simply  in  its  elevation  above  the  earth.     A  fog 
might  be  defined  as  a  cloud  resting  on  the  earth;  and  a 
cloud,  as  a  fog  floating  in  the  air. 

Clouds  are  formed  whenever  a  mass  of  air  away  from 
the  earth's  surface  is  cooled  below  its  dew-point.  This 
cooling  may  be  effected  in  various  ways.  A  cold  wind 
may  penetrate  a  mass  of  warm  air  and  cool  it  below  its 
dew-point,  or  a  warm  moist  wind  may  be  cooled  below  its 
dew-point  by  penetrating  a  mass  of  cold  air.  Ascending 
currents  of  air  are  always  cooled  by  expansion,  and  are 
very  likely  to  give  rise  to  clouds. 


NATURAL   PHILOSOPHY.  461 

558.  Clouds  on  the  Summits  of  Mountains.  —  The  sum- 
mits of  high  mountains  are  usually  enveloped  in  clouds 
even  when  the  rest  of  the  sky  is  clear.  An  interposed 
mountain  forces  a  horizontal  wind  up  to  an  unusual  height 
where  the  temperature  is  low.  When  the  temperature  of 
the  ascending  current  Fig.  481. 

reaches  its  dew-point,  a 
portion  of  its  moisture 
is  condensed  as  a  cloud. 
Let  A  B  C  (Figure  481) 
be  a  mountain  interposed 
in  the  path  of  a  horizon- 
tal current.  The  current 
will  be  forced  upward,  and  made  to  glide  along  the  side  of 
the  mountain.  Let  D  E  represent  the  elevation  at  which 
the  temperature  of  the  ascending  current  will  just  reach 
its  dew-point.  As  soon  as  the  current  passes  above  this 
line  its  vapor  will  be  partially  condensed  so  as  to  form  a 
cloud,  which  will  envelop  the  summit  of  the  mountain. 
As  soon  as  the  current  passes  below  the  line  D  E  on  the 
other  side  of  the  mountain,  its  temperature  again  rises 
above  its  dew-point,  and  the  cloud  is  redissolved.  The 
cloud  is  drifted  by  the  wind,  but  is  not  blown  away  from 
the  mountain  because,  as  fast  as  it  moves  forward,  a  new 
cloud  is  formed  behind  it.  Although  the  cloud  on  the 
mountain  appears  stationary,  the  particles  which  compose 
it  are  continually  changing. 

In  a  similar  manner,  even  in  tolerably  level  countries, 
the  sky  does  not  become  overcast  solely  by  clouds  drifted 
by  the  wind  from  places  beyond  the  horizon.  The  clouds 
are  very  often  formed  in  sight  of  the  observer.  So  too 
the  sky  often  clears,  not  because  the  clouds  are  drifted  off 
by  the  wind,  but  because  they  are  dissipated  by  the  in- 
creasing heat  of  the  air. 

559.    The   Classification   of   Clouds.  —  The    four    chief 


462  NATURAL   PHILOSOPHY. 

varieties  of  clouds  are  the  cirrus,  the  cumulus,  the  stratus, 
and  the  nimbus. 

"The  cirrus  cloud  consists  of  long,  slender  filaments, 
either  parallel  or  diverging  from  each  other,  and  often  pre- 
sents the  appearance  of  a  lock  of  cotton  whose  fibres  are 
electrified  so  as  powerfully  to  repel  each  other.  These 
clouds  appear  to  have  the  least  density,  the  greatest  ele- 
vation, and  the  greatest  variety  of  form.  They  are  gen- 
erally the  first  to  make  their  appearance  after  a  period  of 
perfectly  clear  weather.  Indeed,  in  fair  weather,  the  sky 
is  seldom  entirely  free  from  small  groups  of  cirrus  clouds. 
They  are  believed  to  be  composed  of  spiculae  of  ice  or 
flakes  of  snow  floating  at  a  great  height  in  the  air.  At  the 
height  at  which  they  prevail  the  temperature  of  the  air  is 
below  32°  even  in  midsummer"  (Figure  482). 

Fig.  482. 


"  The  cumulus  cloud  usually  consists  of  a  hemispherical 
or  convex  mass,  rising  from  a  horizontal  base.  It  is  much 
denser  than  the  cirrus,  and  is  formed  in  the  lower  regions 
of  the  atmosphere.  In  fair  weather  the  cumulus  often 
forms  a  few  hours  after  sunrise,  goes  on  increasing  until 
the  hottest  part  of  the  day,  and  disappears  about  sunset. 
We  often  see  near  the  horizon  large  masses  of  cumulus 
clouds,  which  resemble  lofty  mountains  covered  with 
snow. 


NATURAL   PHILOSOPHY.  463 

"  The  rounded  top  of  the  cumulus  results  from  the  mode 
of  its  formation.  When  the  surface  of  the  earth  is  heated 
by  the  rays  of  the  sun,  currents  of  warm  air  ascend,  and  as 
soon  as  they  reach  a  certain  height  a  portion  of  their  vapor 

Fig-  483. 


is  condensed  and  forms  cloud  ;  and  since  the  upward  mo- 
tion is  greatest  under  the  centre  of  the  cloud,  the  vapor  is 
there  carried  up  to  the  greatest  height  "  (Figure  483). 
The  stratus  cloud  is  a  widely  extended  horizontal  sheet, 

Fig.  -(84. 


often  covering  the  sky  with  a  nearly  uniform  veil.  It  is 
the  lowest  of  the  clouds,  and  sometimes  descends  to  the 
surface  of  the  earth  (Figure  484). 

The  nimbus  is  the  well-known  rain-cloud,  consisting  of 


464  NATURAL    PHILOSOPHY. 

a   combination   of    cirrus,    cumulus,    and    stratus    clouds 
(Figure  485). 

Fig.  485- 


mm 


560.  The  Height  and  Thickness  of  Clouds.  — The  height 
of  clouds  is  very  variable.     The  stratus  cloud  sometimes 
descends  to  the  surface  of  the  earth.     In  pleasant  weather 
the  under  surface  of  the  cumulus  cloud  is  from  3000  to 
5000  feet  high.     Cirrus  clouds  are  never  seen  below  the 
summit  of  Mont  Blanc. 

Clouds  are  not  usually  more  than  half  a  mile  thick, 
though  cumulus  clouds  sometimes  attain  a  thickness  of 
3  or  4  miles. 

561.  How  Clouds  are  sustained  in  the  Atmosphere.  —  Since 
clouds  are  composed  of  particles  heavier  than  air,  they 
must  be  slowly  sinking.     They  do  not  ultimately  fall  to 
the  earth  in  pleasant  weather,  because,  as  they  sink,  they 
encounter  warmer  layers  of  air  which  are  not  saturated 
with  vapor.     The  cloud  is  therefore  dissipated  at  the  bot- 
tom as  fast  as  it  falls,  while  it  is  at  the  same  time  renewed 
at  the  top  by  the  condensation  of  vapor  carried  up  by 
ascending  currents. 

562.  Origin  of  Rain.  —  Rain  has  the  same  origin   as 
clouds.    When  the  condensation  takes  place  slowly,  clouds 
only  are  formed  ;  but  when  it  takes  place  with  sufficient 
rapidity,  rain  is  also  formed.     To  produce  an  abundant 


NATURAL    PHILOSOPHY.  465 

rain,  the  air  must  be  suddenly  cooled  below  the  dew-point. 
The  most  effective  way  to  accomplish  this  is  to  force  the 
air  up  a  mile  or  two  above  the  surface  of  the  earth.  Were 
a  mass  of  air  raised  two  miles  from  the  surface  of  the  earth, 
its  temperature  would  fall  about  35°.  The  reduction  of  tem- 
perature would  be  due  partially  to  the  chilling  effects  of 
expansion  and  partially  to  the  coldness  of  the  space  into 
which  the  air  would  be  transported.  Were  the  air  of  the 
surface  of  the  earth  forced  up  to  this  height,  most  of  its 
vapor  would  be  condensed.  The  air  may  be  forced  up- 
ward by  the  interposition  of  a  mountain  range  in  the  path 
of  a  current  of  air,  or  by  the  meeting  of  two  opposing  cur- 
rents. Hence  mountain  ranges  are  very  efficient  con- 
densers of  the  atmospheric  vapor.  The  heaviest  rainfall 
on  the  globe  occurs  where  the  prevailing  wind  is  from  the 
ocean,  and  where  this  wind  is  obliged  to  pass  over  a  high 
mountain  range  on  its  way  to  the  interior  of  the  continent. 
On  the  sheltered  side  of  such  mountain  ranges  there  are 
usually  desert  regions. 

563.  The  Amount  of  Rain  in  Different  Latitudes.  —  The 
average  rainfall  is  greatest  at  the  equator,  and  decreases 
as  we  proceed  towards  the  poles.  The  annual  rainfall  at 
the  equator  is  104  inches ;  in  latitude  20°,  70  inches ;  in 
latitude  30°,  40  inches ;  and  in  latitude  60°,  20  inches. 

The  amount  of  vapor  present  in  the  atmosphere  de- 
creases from  the  equator  to  the  poles,  there  being  about 
five  times  as  much  vapor  present  in  the  atmosphere  at  the 
equator  as  in  latitude  60°.  If  the  causes  which  produce 
rain  acted  with  equal  intensity  in  all  latitudes,  we  should 
expect  that  the  average  rainfall  in  each  latitude  would  be 
proportioned  to  the  amount  of  vapor  present  in  the  atmos- 
phere. This,  on  the  basis  of  104  inches  at  the  equator, 
would  give  90  inches  for  the  latitude  of  20°,  70  inches  for 
the  latitude  of  30°,  and  18  inches  for  the  latitude  of  60°. 
The  actual  rainfall  in  latitude  60°  is  somewhat  higher  than 


466 


NATURAL   PHILOSOPHY. 


the  theoretical  amount;  while  in  latitudes  of  20°  and  30° 
it  is  considerably  less-  We  must  therefore  conclude  that 
the  causes  which  tend  to  produce  rain  act  with  less  intensity 
near  latitude  30°  than  they  do  in  the  neighborhood  of  the 
equator  or  of  latitude  60°.  In  both  of  these  regions  there  is 
an  ascent  of  vast  columns  of  air,  due  in  part  to  the  meeting  of 
opposing  systems  of  winds,  the  trade-winds  in  the  one  case 
and  the  middle-latitude  and  polar  currents  in  the  other. 
The  excessive  condensation  in  these  regions  is  one  cause 
of  the  low  barometer  which  prevails  there. 

Fig.  486. 


564.  Origin  of  Snow.  —  Snow  bears  the  same  relation  to 
rain  that  hoar-frost  does  to  dew.  When  the  vapor  of  the 
atmosphere  is  precipitated  at  a  very  low  temperature,  it  at 
once  assumes  the  solid  state,  usually  in  the  form  of  minute 
crystals.  These  minute  crystals  attach  themselves  to  each 


NATURAL    PHILOSOPHY. 


467 


other  and  form  snow-flakes,  which  fall  slowly  to  the  earth. 
Snow-flakes  present  a  great  variety  of  forms,  some  of 
which  are  shown  in  Figure  486. 

When  the  lower  layers  of  the  atmosphere  are  much 
above  32°,  the  snow-flakes  melt  before  they  reach  the 
ground,  so  that  rain  may  fall  upon  an  open  plain  and  snow 
upon  a  neighboring  mountain,  both  from  the  same  cloud. 

565.  Hail.  —  Large  hail  seldom  if  ever  falls  except  dur- 
ing thunder-storms.  It  very  rarely  follows  rain  which  has 
continued  for  some  time.  The  hail  covers  a  much  smaller 
area  than  the  rain-storm,  and  usually  continues  at  the  same 
place  for  only  five  or  ten  minutes. 

Hailstones  are  of  all  sizes,  from  that  of  small  shot  up  to 
that  of  a  turkey's  egg,  Fig.  487. 

and  of  every  variety  of 
shape.  One  of  very  ir- 
regular form  is  shown  in 
Figure  487.  The  centre 
of  large  hailstones  usu- 
ally consists  of  hardened 
snow,  and  this  is  sur- 
rounded by  a  layer  of 
transparent  ice.  Sometimes  we  find  several  alternate 
layers  of  opaque  snow  and  transparent  ice.  Figure  488 
Fig.  488.  shows  the  section  of  a  Fig.  489. 

hail-stone  whose  exter- 
nal form  is  given  in 
Figure  489. 

566.  Origin  of  Hail. 
—  "  The  formation  of 
hail  is  invariably  at- 
tended by  two  distinct  currents  of  air,  and  one  of  these 
currents  displaces  the  other  with  great  violence.  The  cur- 
rent of  air  which  precedes  the  approach  of  a  hail-storm  is 
extremely  hot,  and  highly  charged  with  moisture  ;  and  that 


468  NATURAL    PHILOSOPHY. 

which  succeeds  the  fall  of  hail  has  an  icy  chillness.  The 
warm  and  humid  air  is  displaced  by  the  cold  current,  and 
is  thus  forced  up  to  a  great  elevation  above  the  earth,  by 
which  means  its  vapor  is  suddenly  condensed.  Upon  the 
front  of  the  hail-cloud  this  condensed  vapor  exists  in  the 
form  of  water,  whose  temperature  is  near  32°.  In  the  in- 
terior of  the  hail-cloud  the  vapor  is  precipitated  in  the 
form  of  snow,  whose  temperature  is  sometimes  as  low 
as  20°. 

"  Observations  on  the  summits  of  mountains  have  shown 
that  on  the  front  of  the  hail-cloud  there  exists  a  violent  whirl- 
ing motion  about  a  horizontal  axis.  This  whirling  motion 
causes  the  snow  to  collect  in  small  balls,  each  of  which 
forms  the  nucleus  of  a  hailstone.  The  snow-ball  is  forced 
into  the  warm  current,  where  it  receives  a  layer  of  water, 
which  is  congealed  by  the  nucleus,  thus  rendering  the 
snowy  centre  more  compact,  and  adding  a  shell  of  trans- 
parent ice.  By  means  of  the  whirling  motion,  the  hail- 
stone, covered  with  a  stratum  of  uncongealed  water,  is 
hurled  into  the  snow-cloud,  where  it  receives  a  layer  of 
snow,  and  again  becomes  thoroughly  chilled.  Thence  it 
escapes  again  into  the  water-cloud,  and  is  covered  with  a 
layer  of  water,  which  is  congealed  by  the  cold  of  the  nu- 
cleus. Thus,  by  the  whirling  motion,  it  is  plunged  alter- 
nately into  the  snow-cloud  and  the  water-cloud,  while  each 
alternation  furnishes  a  layer  of  spongy  ice  and  a  layer  of 
transparent  ice.  Thus  the  stone  grows  with  immense 
rapidity,  and  in  a  few  minutes  becomes  a  large  ball  three 
or  four  inches  in  diameter. 

"  The  hailstones  are  sustained  in  the  air  by  the  violent 
upward  motion  caused  by  the  cold  current  displacing  the 
warm  one.  A  sphere  of  ice  two  inches  in  diameter,  by- 
falling  through  a  tranquil  atmosphere,  soon  acquires  a 
velocity  of  90  feet  per  second.  A  hailstone  of  irregular 
shape  would  experience  more  resistance  than  a  sphere,  and 


NATURAL    PHILOSOPHY.  469 

would  acquire  a  somewhat  less  velocity,  but  it  would  still 
fall  from  a  height  of  18,000  feet  in  about  three  minutes, 
which  time  is  too  small  to  allow  the  formation  of  masses  of 
ice  weighing  one  pound.  An  upward  current  of  air,  rising 
with  a  velocity  of  90  feet  per  second,  would  sustain  a 
sphere  of  ice  two  inches  in  diameter,  and  would  greatly 
reduce  the  velocity  of  stones  of  larger  size." 

D.  STORMS. 

567.  Origin  of  Storms.  —  Any  violent  and  extensive  com- 
motion of  the  atmosphere  is  called  a  storm.  Such  commo- 
tions are  usually  attended  by  a  fall  of  rain,  snow,  or  hail, 
but  the  storm  often  extends  beyond  the  area  of  snow  or 
rain,  and  even  beyond  the  area  of  clouds. 

Storms  are  caused  by  a  strong  and  extensive  upward  mo- 
tion of  the  air.  Since  the  air  is  heated  by  contact  with  the 
earth,  and  by  absorption  of  solar  and  terrestrial  radiations 
by  the  watery  vapor  in  it,  the  atmosphere  is  heated  chiefly 
at  the  bottom,  the  watery  vapor  existing  chiefly  in  the 
lower  layers.  An  excessive  heating  of  a  mass  of  air  at  the 
surface  of  the  earth,  either  by  contact  with  a  hot  surface  or 
by  an  unusually  large  absorption,  due  to  an  excess  of 
moisture,  gives  rise  to  a  system  of  currents  such  as  has 
been  already  described.  A  vertical  section  of  this  system 
of  currents  is  shown  in 
Figure  490 ;  a  horizon- 
tal section  at  the  bottom, 
in  Figure  491  ;  and  a 
horizontal  section  at  the 
top,  in  Figure  492. 

As  the  air  in  the  centre  of  the  area  rises,  it  is  cooled  by 
expansion  at  the  rate  of  about  38°  for  every  two  miles  of 
ascent.  The  height  to  which  the  air  will  have  to  rise  to  be 
cooled  to  its  dew-point  depends  upon  the  difference  be- 
tween the  dew-point  and  the  temperature  of  the  air.  As 


470  NATURAL    PHILOSOPHY. 

soon  as  the  cloud  begins  to  form,  the  latent  heat  of  the 
vapor  is  liberated.     A  rainfall  of   one   inch   precipitates 

Fig.  491. 


over  two  million  cubic  feet  of  water  upon  one  square  mile 
of  surface,  and  liberates  as  much  heat  over  the  square  mile 
as  it  would  take  to  evaporate  two  million  cubic  feet  of  wa- 
ter. It  takes  over  60,000  units  of  heat  to  evaporate  one 
Fig.  492-  cubic  foot  of  water.  The  heat 

thus  liberated  warms  the  air  in 
the  region  in  which  the  conden- 
sation takes  place,  and  causes 
the  mass  of  air  to  rise  still 
higher.  As  the  air  rises  higher, 
more  of  its  vapor  is  condensed 
and  more  heat  is  liberated. 

The  expansion  of  the  col- 
umn of  air  ascending  in  the 
centre  of  a  storm,  especially  after  heat  begins  to  be  liber- 
ated by  the  condensation,  causes  the  air  to  spread  out  in 
all  directions  above,  making  a  barometer  under  the  centre 
of  the  cloud  fall  below  its  mean  height,  and  one  beyond 
the  limits  of  the  cloud  rise  above  its  mean  height.  Near 
the  limits  of  the  cloud  the  air,  being  heavier,  sinks  down- 
ward, and  a  portion  of  it  flows  along  the  surface  towards 
the  centre  of  the  ascending  column,  while  another  portion 


NATURAL   PHILOSOPHY.  471 

flows  along  the  surface  in  the  opposite  direction,  producing 
a  gentle  breeze  away  from  the  cloud.  The  air  spreads  out 
more  rapidly  above  than  it  runs  in  below,  and  the  storm 
tends  to  increase  in  diameter.  Storms  often  extend  with 
great  rapidity  till  they  cover  an  area  of  more  than  a  thou- 
sand miles  in  diameter. 

When  a  storm  arises  some  distance  to  the  north  of  the 
equator,  the  surface  currents  which  set  in  towards  its  cen- 
tre are  deflected  to  the  right,  and  so  the  wind  blows  in 
spirally  towards  the  centre.  This  circulation  of  the  wind 
around  the  centre  of  the  storm  gives  rise  to  a  centrifugal 
force  which  tends  to  whirl  the  air  out  from  the  centre  above 
and  to  increase  the  fall  of  the  barometer.  The  fall  of  the 
barometer  in  the  centre  of  a  storm  is  largely  due  to  the 
circulation  of  the  air  around  a  rain-area;  but  the  chief 
agent  in  originating  the  disturbance  is  the  rainfall  itself. 
As  soon  as  the  rain  ceases,  the  force  of  the  wind  declines, 
and  the  barometer  recovers  its  mean  height. 

568.  The  Development  and  Motion  of  Storms.  —  Storms 
begin  gradually,  and  are  usually  a  day  or  two  in  attaining 
their  greatest  violence.  After  a  day  or  two  longer  their 
violence  again  decreases,  and  at  length  they  disappear  or 
are  merged  into  other  storms.  A  storm  occasionally  holds 
out  one  or  two  weeks,  but  it  usually  lasts  only  a  few  days. 
A  storm  sometimes  remains  nearly  stationary  for  a  day  or 
two,  but  it  usually  moves  eastward  about  600  miles  a  day ; 
and  though  the  same  storm  may  continue  in  existence  one 
or  two  weeks,  it  seldom  lasts  more  than  one  or  two  days  at 
the  same  place. 

The  average  direction  of  storms  across  the  United  States 
is  a  little  north  of  east,  being  almost  exactly  east  during 
the  summer.  Storms  occasionally  deviate  greatly  from 
their  usual  track,  sometimes  moving  towards  the  northeast, 
sometimes  towards  the  southeast,  and  occasionally  due 
north. 


472  NATURAL    PHILOSOPHY. 

The  average  velocity  of  storms  is  twenty-six  miles  an 
hour,  being  twenty-one  in  the  summer  and  thirty  in  the 
winter.  They  occasionally  move  at  the  rate  of  fifty  miles 
an  hour,  and  sometimes  remain  almost  stationary  for  a  day 
or  two. 

The  direction  in  which  a  storm  moves  is  entirely  distinct 
from  that  of  the  wind  which  accompanies  it.  While  the 
storm  moves  steadily  eastward,  the  wind  has  every  possible 
direction  at  places  within  the  limits  of  the  storm.  At 
places  on  the  north  side  of  the  centre  of  the  storm  the 
wind  usually  sets  in  from  the  northeast  as  the  storm  ap- 
proaches, and  veers  round  by  the  north  to  the  northwest 
as  the  storm  passes  over.  At  places  on  the  south  side  of 
the  centre  the  wind  generally  sets  in  from  the  southeast, 
and  then  veers  round  by  the  south  to  the  southwest. 

Near  the  centre  of  a  great  storm  there  is  usually  a  lull 
in  the  wind,  and  sometimes  a  calm.  There  is  seldom  any 
rain,  and  the  clouds  often  break,  and  occasionally  there  is 
a  clear  sky  for  several  hours.  Soon  after  the  centre  of  the 
storm  has  passed  the  wind  changes  to  the  west,  and  there 
is  a  heavy  fall  of  rain  or  snow  of  comparatively  short 
duration. 

The  winds  on  the  east  side  of  a  storm  are  propagated  in 
a  direction  opposite  to  that  in  which  they  blow.  That  is 
to  say,  they  are  propagated  eastward  while  they  blow 
westward.  Winds  propagated,  like  these,  in  the  opposite 
direction  to  that  in  which  they  blow  are  said  to  be  propa- 
gated by  aspiration.  The  winds  on  the  west  of  the  storm 
are  propagated  in  the  same  direction  as  that  in  which 
they  blow.  Such  winds  are  said  to  be  propagated  by 
impulsion. 

569.  Motion  of  the  Air  within  Areas  of  Low  and  High 
Barometer.  —  "  It  is  found  that  within  the  limits  of  the 
United  States,  around  every  storm-centre,  the  wind  moves 
spirally  inward,  circulating  about  the  centre  in  a  direction 


NATURAL    PHILOSOPHY. 


473 


contrary  to  the  motion  of  the  hands  of  a  watch,  and  the 
average  inclination  of  the  winds  to  a  radius  drawn  from 
the  centre  of  the  storm  is  almost  exactly  45°. 

"  On  the  contrary,  within  an  area  of  high  barometer  the 
winds  blow  outward,  and  the  average  inclination  of  the 
winds  to  a  radius  drawn  from  the  centre  of  the  area  is 
also  about  45°,  but  the  winds  circulate  about  the  centre 
of  the  area  in  the  same  direction  as  that  of  the  hands  of  a 
watch.  The  former  motion,  being  in  the  same  direction  as 
that  observed  in  violent  cyclones,  is  called  cyclonic ;  and  the 
latter  motion,  being  in  the  opposite  direction,  is  called 
anti-cyclonic. ' ' 

570.  Cyclones.  —  "  The  inequalities  of  the  earth's  sur- 
face, especially  in  hilly  countries,  greatly  modify  the  direc- 
tion of  the  wind,  so  that  in  great  storms  the  movements 
of  the  atmosphere  often  seem  very  complex  and  anom- 
alous. Over  the  ocean  these  disturbing  causes  do  not 
exist,  and  here  we  find  that  in  violent  storms  the  move- 
ments of  the  air  are  much  more  regular  and  uniform. 
This  motion  of  the  wind  has  generally  been  found  to  be 
in  great  circuits,  spirally  inward  toward  the  centre  of  the 
storm,  and  such  storms  are  now  commonly  designated  by 
the  term  cyclone.  These 
storms  prevail  in  the 
neighborhood  of  the 
West  India  Islands, 
where  they  have  long 
been  known  by  the  name 
of  hurricanes.  They  are 
also  common  in  the  China 
Sea  and  in  the  Indian 
Ocean,  on  both  sides  of 
the  equator." 

Cyclones    originate 
near  the  equatorial  lim- 


474  NATURAL    PHILOSOPHY. 

its  of  the  trade-winds  on  either  side  of  the  equator,  and 
move  northward  and  southward  in  parabolic  paths,  as 
shown  in  Figure  493.  The  small  arrows  indicate  the  di- 
rection of  the  circulation  of  the  wind  in  the  cyclone  itself. 
Tornadoes  are  only  very  violent  storms,  caused  by  a  sud- 
den and  very  great  fall  of  pressure. 

571.  Predictions  foimded  ttpon  the  Established  Laws  of 
Storms.  — "  The  laws  of  storms  are  now  so  well  under- 
stood that  we  can  predict  with  some  confidence  the 
changes  which  will  succeed  at  any  place  during  the  next 
few  hours,  provided  we  can  know  the  state  of  the  weather 
throughout  the  surrounding  region  to  a  great  distance. 
This  is  what  has  been  attempted  since  1871  by  the  United 
States  Signal  Service,  and  the  general  accuracy  of  these 
predictions  has  excited  considerable  surprise.  Such  pre- 
dictions would  be  still  more  reliable  if  we  could  have 
information  respecting  the  various  meteorological  elements 
from  a  larger  portion  of  the  earth's  surface.  The  centre 
of  a  large  portion  of  our  storms  follows  nearly  the  northern 
boundary  of  the  United  States,  so  that  our  observations 
inform  us  respecting  only  one  half,  or  perhaps  less  than 
one  half,  of  the  storm-area.  Moreover,  storms  are  often 
affected  by  changes  which  are  going  on  in  very  distant 
quarters.  An  area  of  unusually  high  barometer  may 
affect  the  course  of  a  storm  whose  centre  is  distant  two  or 
three  thousand  miles;  and  an  unusual  fall  of  rain  in  the 
equatorial  regions  may  cause  an  unusual  overflow  of  air 
to  the  middle  latitudes,  resulting  in  serious  disturbances  of 
atmospheric  pressure.  When  the  laws  of  storms  have  been 
more  precisely  defined,  and  telegraphic  reports  can  be 
received  from  a  more  extended  area,  we  shall  doubtless 
be  able  to  predict  coming  storms  with  greater  precision." 


NATURAL   PHILOSOPHY.  475 


VI. 

ELECTRICAL  PHENOMENA  OF  THE  ATMOS- 
PHERE. 

A.     ATMOSPHERIC  ELECTRICITY. 

572.  Electrical  Condition  of  the  Atmosphere. — The  atmos- 
phere is  almost  always  charged  with  electricity,  and  usually 
with  positive  electricity.  There  are,  however,  great  varia- 
tions in  the  intensity  of  the  charge,  and  clouds  are  fre- 
quently charged  with  negative  electricity. 

The  intensity  of  atmospheric  electricity  varies  regularly 
with  the  hour  of  the  day  and  with  the  season  of  the  year. 
During  the  day  it  is  least  intense  at  4  A.  M.  and  at  4  P.  M., 
and  most  intense  at  10  A.M.  and  at  10  P.M.  It  is  least 
intense  during  the  summer  months  and  most  intense  dur- 
ing the  winter  months.  The  intensity  of  atmospheric  elec- 
tricity also  increases  with  the  altitude  above  the  surface  of 
the  earth. 

When  the  sky  is  covered  with  clouds  there  are  frequent 
changes  in  kind  as  well  as  in  intensity  of  atmospheric 
electricity,  the  atmospheric  being  sometimes  positive  and 
sometimes  negative.  It  is  seldom  negative,  however,  ex- 
cept when  rain  is  falling.  When  snow  is  falling,  the  lower 
layer  of  air  becomes  highly  charged  with  electricity.  Dur- 
ing a  thunder-shower  the  electricity  of  the  air  frequently 
changes  in  two  or  three  minutes  from  positive  to  negative, 
and  back  to  positive  again,  and  sometimes  half  a  dozen  of 
these  changes  occur  during  a  single  shower. 

573.  Origin  of  Atmospheric  Electricity.  —  The  following  ac- 
count of  the  origin  of  atmospheric  electricity  is  taken  from 
Loomis :  "Evaporation  is  probably  the  principal  source  of 
atmospheric  electricity.  The  following  experiment  shows  the 
production  of  electricity  by  evaporation.  If  upon  the  top  of  a 


476  NATURAL    PHILOSOPHY. 

gold-leaf  electrometer  \ve  place  a  metallic  vessel  containing  salt 
water,  and  drop  into  the  water  a  heated  pebble,  the  leaves  of  the 
electrometer  will  diverge.  The  vapor  which  rises  from  the  water 
is  charged  with  positive  electricity,  while  the  water  retains  neg- 
ative electricity. 

"  The  water  used  in  this  experiment  must  not  be  perfectly 
pure,  but  must  contain  a  little  salt,  or  some  foreign  matter.  The 
evaporation  of  the  water  of  the  ocean  must  therefore  furnish  a 
large  amount  of  electricity,  and  fresh  water  must  also  furnish 
some  electricity,  for  the  water  of  the  earth  is  never  entirely 
pure. 

"  The  diurnal  variation  in  the  intensity  of  atmospheric  elec- 
tricity is  to  be  ascribed  partly  to  real  changes  in  the  amount  of 
electricity  present  in  the  air,  and  partly  to  variations  in  the  con- 
ducting power  of  the  air. 

"Just  before  sunrise  the  electricity  has  a  feeble  intensity, 
because  the  moisture  of  the  preceding  night  has  transmitted  to 
the  earth  a  portion  of  the  electricity  which  was  previously  present 
in  the  air.  After  the  sun  rises,  new  vapor  ascends  and  carries 
with  it  positive  electricity,  so  that  the  amount  of  electricity  in 
the  air  increases.  Toward  noon  the  air  becomes  dry,  and  trans- 
mits less  readily  the  electricity  accumulated  in  the  upper  regions 
of  the  atmosphere ;  so  that,  although  the  amount  of  electricity 
in  the  air  is  continually  increasing,  an  electrometer  near  the 
earth's  surface  indicates  an  apparent  diminution. 

"  Toward  evening  the  air  grows  cool,  again  becomes  humid, 
and  transmits  more  readily  to  the  earth  the  electricity  accumu- 
lated in  the  upper  regions  of  the  atmosphere.  The  effect  pro- 
duced upon  an  electrometer  therefore  increases  until  some  hours 
after  sunset ;  but  since  during  the  night  there  is  a  constant  dis- 
charge of  electricity  from  the  air  to  the  earth  the  electrometer 
soon  indicates  a  diminished  intensity,  which  continues  until 
towards  morning. 

"  The  same  principle  explains  why  the  electricity  of  the  air 
appears  less  intense  in  summer  than  in  winter.  In  summer  the 
air  is  warm  and  dry,  and  opposes  more  resistance  to  the  flow  of 
electricity  from  the  higher  regions  of  the  atmosphere,  while  in 
winter  the  moist  air  produces  a  contrary  effect ;  so  that,  although 
the  atmosphere  doubtless  contains  more  electricity  in  summer 


NATURAL   PHILOSOPHY.  477 

than  in  winter,  it  generally  produces  a  less  effect  upon  an  elec- 
trometer placed  near  the  earth's  surface. 

"  We  have  found  that  the  atmosphere  ordinarily  contains  a 
large  quantity  of  electricity.  Since  dry  air  is  a  non-conductor, 
the  electrified  particles  in  clear  weather  are  in  a  measure  insu- 
lated, and  the  electricity  cannot  acquire  much  intensity;  but 
when  the  vapor  of  the  air  is  precipitated  and  a  cloud  is  formed, 
the  electricity  which  was  previously  confined  to  the  separate 
particles  of  the  air  now  finds  a  conducting  medium  more  or  less 
perfect,  and  it  spreads  itself  over  the  surface  of  the  cloud, 
thereby  acquiring  considerable  intensity.  It  is  generally  ad- 
mitted that  the  same  quantity  of  electricity  which  exists  in  the 
cloud  existed  in  the  air  before  the  formation  of  the  cloud,  and 
that  the  cloud  performs  no  other  office  than  that  of  a  conductor. 

"  A  cloud  thus  electrified  must  necessarily  have  positive 
electricity,  since  in  clear  weather  the  electricity  of  the  atmos- 
phere is  always  positive.  Such  a  cloud,  when  it  approaches 
near  another  cloud  having  less  electricity,  or  none  at  all.  acts 
by  induction  upon  the  latter,  decomposing  its  natural  electricity, 
attracting  the  negative  electricity  and  repelling  the  positive. 
The  positive  electricity  thus  repelled  may  be  sometimes  drawn 
off  by  near  approach  to  another  cloud,  or  to  the  earth,  leaving 
only  negative  electricity  upon  the  cloud.  Hence  probably  result 
the  frequent  alternations  of  positive  and  negative  electricity  ob- 
served during  a  thunder-shower." 

B.   LIGHTNING. 

574.  Lightning.  —  "Two  clouds  having  opposite  electri- 
cities attract  each  other,  and  when  the  clouds  come  suffi- 
ciently near,  the  two  electricities  rush  towards  each  other 
with  great  violence.  This  phenomenon  is  called  lightning, 
and  is  accompanied  by  an  explosive  noise  called  thunder. 

"  Since  clouds  are  very  imperfect  conductors,  when  the 
electricity  of  one  part  of  a  cloud  is  discharged,  the  elec- 
tricity of  a  distant  part  of  the  cloud  is  but  slightly  changed. 
Thus,  a  single  discharge  does  not  establish  a  complete 
electrical  equilibrium  ;  but  there  is  a  change  in  the  distri- 


478  NATURAL    PHILOSOPHY. 

bution  of  the  electricities  upon  the  surrounding  clouds, 
and  there  must  be  a  succession  of  discharges  before  the 
electricity  is  entirely  neutralized.  Hence  results  a  succes- 
sion of  flashes  of  lightning  and  peals  of  thunder. 

"A  cloud  charged  with  electricity  exerts  an  inductive 
influence  upon  the  earth's  surface  immediately  beneath  it, 
decomposing  its  natural  electricities,  repelling  electricity  of 
the  same  kind,  and  attracting  the  opposite  kind.  Accord- 
ingly there  will  sometimes  be  a  discharge  of  electricity 
from  the  cloud  to  the  earth.  This  charge  is  usually  re- 
ceived by  the  most  elevated  objects,  such  as  mountains, 
hills,  trees,  spires,  high  buildings,  etc.  Trees  are  particu- 
larly exposed  to  strokes  of  lightning  on  account  of  their 
elevation,  as  well  as  of  the  moisture  which  they  contain, 
and  which  renders  them  partial  conductors  of  electricity." 

575.  Lightning-Rods.  —  Buildings  may  be  protected  from 
injury  by  the  use  of  lightning-rods.  These  are  metallic 
rods  running  from  the  top  of  the  building  to  the  ground. 
The  rods  must  not  be  too  small,  and  their  parts  must  be 
well  connected  so  as  tp  be  in  good  metallic  contact.  They 
should  run  well  into  the  earth  at  the  bottom,  and  be  care- 
fully pointed  at  the  top.  There  ought  to  be  several  sets  of 
points  on  the  top  of  the  building  connected  by  metallic 
rods  with  each  other  and  with  the  rod  that  runs  to  the 
ground ;  and  if  the  building  is  at  all  large  there  ought  to 
be  several  rods  running  to  the  ground,  all  connected  to- 
gether by  metallic  rods.  If  the  building  has  a  metallic 
roof,  or  there  are  metallic  pipes  or  other  masses  of  metal 
in  the  interior,  these  should  all  be  carefully  connected  with 
the  rod.  The  points  are  designed  to  facilitate  the  escape 
of  the  electricity  from  the  building  and  the  ground  around 
it  when  these  are  acted  upon  inductively  by  the  cloud,  so 
as  to  prevent  electricity  from  accumulating  upon  them. 
This  accumulation  of  electricity  upon  an  object  always 
precedes  a  violent  discharge  between  it  and  the  cloud ; 


NATURAL   PHILOSOPHY. 


479 


and  if  the  accumulation  can  be  prevented  no  violent  dis- 
charge will  take  place.  Should  the  electricity  be  developed 
by  induction  more  rapidly  than  it  can  escape  silently  from 
the  poinls,  and  a  spark  discharge  should  take  place,  the 
rod  serves  as  the  path  of  least  resistance,  and  the  discharge 
will  take  this  path  rather  than  pass  through  the  building, 
which  offers  greater  resistance. 

576.  Forms  of  Lightning.  —  "  Lightning  exhibits  a  variety 
of  forms,  which  have  been  designated  by  the  terms  zigzag, 
ball,  sheet,  and  heat  lightning. 

"  Zigzag  lightning  presents  a  long,  irregular,  jagged  line 
of  light,  like  the  ordinary  spark  drawn  from  an  electric 
machine.  This  zigzag  path  is  sometimes  four  or  five  miles, 
and  perhaps  even  ten  miles  in  length." 

"  Ball  lightning  appears  like  a  ball  of  fire,  and  is  usually 
accompanied  by  a  terrific  explosion.  It  probably  results 
from  a  charge  of  electricity  unusually  intense,  which  forces 
a  direct  instead  of  a  circuitous  passage  through  the  air. 

"  Some  have  supposed  that  ball  lightning  was  the  ag- 
glomeration of  ponderable  substances  in  a  state  of  great 
tenuity,  strongly  charged  with  electricity." 

'•'•Sheet  lightning  is  a  diffuse  glare  of  light,  sometimes 
illuminating  only  the  edges  of  a  cloud,  and  sometimes 
spreading  over  its  entire  surface. 

"This  may  be  sometimes  due  to  distant  lightning  which 
illumines  a  cloud,  while  the  direct  flash  is  hidden  from  the 
observer  by  intervening  clouds.  Sometimes  it  may  result 
from  a  movement  of  electricity  in  the  interior  of  a  cloud 
which  is  a  very  imperfect  conductor,  producing  an  illumi- 
nation analogous  to  that  observed  on  a  plate  of  moist 
glass  employed  in  discharging  an  electrical  machine. 

"  During  the  evenings  of  summer  the  horizon  is  some- 
times illumined  for  hours  in  succession  by  flashes  of  light 
unattended  by  thunder.  This  is  called  heat  lightning. 
This  illumination  is  sometimes  due  to  the  reflection  from 


480  NATURAL   PHILOSOPHY. 

the  atmosphere  of  the  lightning  of  clouds  so  distant  that 
the  thunder  cannot  be  heard. 

"  Sometimes,  however,  this  light  overspreads  the  entire 
heavens,  showing  that  the  electricity  of  the  clouds  escapes 
in  flashes  so  feeble  that  they  produce  no  audible  sound. 
Such  cases  may  occur  when  the  air  is  very  moist,  the  air 
being  then  a  tolerable  conductor,  and  offering  just  sufficient 
resistance  to  the  passage  of  the  electricity  to  develop  a 
feeble  light." 

577.  Thunder.  —  The  light  of  lightning  proceeds  from 
the  air,  which  is  heated  white-hot  along  the  line  of  dis- 
charge by  the  passage  of  the  electricity.  The  thunder 
seems  to  be  the  noise  produced  by  the  sudden  expansion 
and  contraction  of  this  heated  line  of  air. 

Sound  travels  only  noo  feet  a  second,  while  the  trans- 
mission of  light  is  nearly  instantaneous.  Hence  the  sound 
does  not  reach  the  ear  until  some  time  after  the  flash  is 
seen.  By  observing  the  interval  between  the  flash  and  the 
report,  the  distance  of  the  point  of  discharge  can  be  as- 
certained, sound  travelling  a  mile  in  about  five  seconds. 
Thunder  is  seldom  heard  more  than  ten  miles  away. 

The  sound  is  produced  instantaneously  at  every  point 
along  the  line  of  the  flash,  but,  since  different  parts  of  the 
flash  are  usually  at  unequal  distances  from  the  observer, 
the  sound  from  different  points  will  reach  the  ear  in  slow 
succession,  producing  a  prolonged  peal  of  thunder.  The 
prolonged  duration  of  some  peals  of  thunder  is  in  part 
due  to  echoes,  produced  by  reflection  from  the  sides  of 
mountains  or  from  clouds. 

The  variable  intensity  or  rolling  of  thunder  is  due  partly 
to  the  zigzag  course  of  the  discharge,  which  often  brings 
several  points  of  the  flash  equally  distant  from  the  ob- 
server (the  sounds  from  these  points  reach  the  ear  simul- 
taneously, and  so  produce  a  sound  of  double  and  triple  the 
intensity);  and  partly  to  the  unequal  distance  of  different 


NATURAL    PHILOSOPHY.  481 

parts  of  the  flash,  the  sound  decreasing  in  intensity  as  the 
square  of  the  distance  increases.  The  rolling  of  thunder 
is  in  part  also  the  effect  of  echoes. 

Thunder  often  begins  with  a  rattling  sound,  followed  by 
a  loud  peal  of  variable  intensity,  and  ends  with  a  low  rat- 
tling sound.  This  succession  of  sounds  may  be  due  to  a 
discharge  like  that  represented  in  Figure  494.  An  observer 
at  E  would  first  hear  a  rattling  sound  from  the  branches 
A  Ct  A  C1,  etc.,  from  the  first  cloud,  and  then  a  loud 

Fig-  494- 


crash  of  variable  intensity  from  the  concentrated  discharge 
between  A  and  B,  and  finally  a  rumbling  sound  from  the 
branches  B  £>,  B  Z>',  etc.,  of  the  distant  cloud,  the  noise 
being  feeble  on  account  of  the  great  distance. 

C.  THE  AURORA. 

578.  The  Polar  Light.  —  The  polar  light  is  a  luminous 
appearance  frequently  seen  near  the  horizon  as  a  diffused 
light,  similar  to  that  of  the  dawn,  whence  it  has  received 
the  name  of  aurora. 

579.  Varieties.  —  "  Auroras  exhibit  an  infinite  variety  of 
appearances,  but  they  may  be  generally  referred  to  one 
of  the  following  classes  :  — 

"  First.  A  horizontal  light  like  the  morning  aurora   or 
break  of  day.     The  polar  light  may  generally  be  distin- 


482 


NATURAL    PHILOSOPHY. 


guished  from  the  true  dawn  by  its  position  in  the  heavens, 
since  in  the  United  States  it  always  appears  in  the 
northern  quarter. 

"  Second.  An  arch  of  light  somewhat  in  the  form  of  a 
rainbow.     This    arch    frequently   extends    entirely  across 


the  heavens  from  east  to  west,  and  cuts  the  magnetic 
meridian  nearly  at  right  angles.  This  arch  does  not  long 
remain  stationary,  but  frequently  rises  and  falls  ;  and  when 

Fig.  496. 


the  aurora  exhibits  great  splendor  several  parallel  arches 
are  often  seen  at  the  same  time,  appearing  as  broad  belts 
of  light,  stretching  from  the  eastern  to  the  western  hori- 
zon (Figure  495). 


NATURAL   PHILOSOPHY.  483 

"The  auroral  arches  exhibit  great  varieties  of  form, 
sometimes  presenting  the  appearance  of  a  brilliant  curtain, 
whose  folds  are  agitated  by  the  wind  (Figure  496.) 

"  Third.  Slender,  luminous  beams  or  columns,  well  defined, 
and  often  of  a  bright  light.  These  beams  rise  to  various 
heights  in  the  heavens,  from  20°  or  30°  up  to  90°  or  more, 
sometimes,  though  rarely,  passing  the  zenith.  Their 
breadth  varies  from  a  quarter  of  a  degree  up  to  two  or 
three  degrees.  Frequently  they  last  but  a  few  minutes, 
sometimes  they  continue  a  quarter  of  an  hour,  a  half- 
hour,  or  even  a  whole  hour.  Sometimes  they  remain  at 
rest,  and  sometimes  they  have  a  quick  lateral  motion. 
This  light  is  commonly  of  a  pale  yellow,  sometimes  red- 
dish, occasionally  crimson,  or  even  of  blood  color.  Some- 
times the  luminous  beams  are  interspersed  with  dark  rays 
resembling  dense  smoke.  Sometimes  the  tops  of  the 
beams  are  pointed,  and,  having  a  waving  motion,  they 
resemble  the  lambent  flames  of  half-extinguished  alcohol 
burning  upon  a  broad  flat  surface. 

"  Fourth.  Luminous  beams  sometimes  shoot  up  simul- 
taneously from  nearly  every  part  of  the  horizon,  and  con- 
verge to  a  point  a  little  south  of  the  zenith,  forming  a 
quivering  canopy  of  flame,  which  is  called  the  corona.  The 
sky  now  resembles  a  fiery  dome,  and  the  crown  appears  to 
rest  upon  variegated  fiery  pillars  which  are  frequently  trav- 
ersed by  waves  or  flashes  of  light.  This  may  be  called  a 
complete  aurora,  and  comprehends  most  of  the  peculiarities 
of  the  other  varieties. 

"Fifth.  Waves  or  flashes  of  light.  The  luminous 
beams  sometimes  appear  to  shake  with  a  tremulous  mo- 
tion, flashes  like  waves  of  light  roll  up  toward  the  zenith, 
and  sometimes  •  travel  along  the  line  of  an  auroral  arch. 
Sometimes  the  beams  have  a  slow  lateral  motion  from  east 
to  west,  and  sometimes  from  west  to  east.  These  sudden 
flashes  of  auroral  light  are  known  by  the  name  of  merry 


484 


NATURAL   PHILOSOPHY. 


dancers,  and  form   an  important  feature  of   nearly  every 
splendid  aurora." 

580.  Height  and  Distribution  of  Auroras.  —  From  a  large 
number  of  observation's,  it  is  concluded  that  the  aurora  seldom 
appears  at  a  less  elevation  than  45  miles  from  the  earth's  sur- 

Fig.  497. 


face,  and  that  it  frequently  extends  upward  to  an  elevation  of 
500  miles.  Auroras  occur  most  frequently  in  the  higher  lati- 
tudes, and  are  seldom  seen  within  the  tropics.  In  North  Amer- 
ica they  are  most  frequent  between  latitudes  50°  and  60°.  In 


NATURAL   PHILOSOPHY.  485 

this  belt  they  are  seen  almost  every  night,  and  they  appear  high 
in  the  heavens.  Farther  north  they  are  less  frequent,  and  are 
seldom  seen  except  towards  the  south.  The  belt  of  greater 
auroral  activity  in  the  northern  hemisphere  is  shown  in  Figure 
497.  It  is  farther  north  in  Europe  than  in  America.  It  bears 
considerable  resemblance  in  form  to  a  magnetic  parallel. 

Auroras  are  as  numerous  in  the  southern  hemisphere  as  in 
the  northern,  and  probably  have  a  corresponding  geographical 
distribution.  Probably  all  great  auroral  displays  take  place 
simultaneously  in  both  hemispheres. 

581.  Periodicity  of  Auroras.  —  There  is  a  diurnal,  an  an- 
nual, and  a  secular  periodicity  in  auroral  displays.  The  maxi- 
mum frequency  and  brilliancy  of  auroras  during  the  day  occurs 
about  midnight,  and  during  the  year  from  April  to  September. 
The  annual  maximum  is  less  evident,  because  of  the  shorter 
evenings,  but  careful  observation  shows  that  there  is  a  decided 
diminution  in  the  frequency  of  auroras  during  the  winter.  The 
grandest  displays  of  the  aurora  occur  at  intervals  of  about  60 
years,  while  a  less  marked  periodic  fluctuation  occurs  every 
10  years.  These  two  periods  of  secular  variation  in  the  aurora 
correspond  in  a  remarkable  manner  with  those  of  the  daily 
fluctuation  of  the  magnetic  needle  and  those  of  sun-spot 
frequency. 

582  Theory  of  the  Polar  Light.  —  The  following  account  of 
the  theory  of  the  aurora  is  abridged  from  Loomis,  with  slight 
changes  of  expression  :  — 

Auroral  exhibitions  take  place  in  the  upper  regions  of  the 
atmosphere  and  partake  of  the  earth's  rotation.  All  the  celes- 
tial bodies  have  an  apparent  motion  from  east  to  west,  arising 
from  the  rotation  of  the  earth  ;  but  bodies  belonging  to  the 
earth,  including  the  atmosphere  and  the  clouds  which  float  in  it, 
partake  of  this  rotation,  so  that  their  relative  position  is  not 
affected  by  it.  The  same  is  true  of  the  aurora.  Whenever  a 
corona  is  formed,  it  maintains  sensibly  the  same  position  in  the 
heavens  during  the  whole  period  of  its  continuance,  although 
the  stars  meanwhile  revolve  at  the  rate  of  15°  per  hour. 

The  colors  of  the  aurora  are  the  same  as  those  of  ordinary 
electricity  passed  through  rarefied  air.  When  a  spark  is  drawn 
from  an  ordinary  electrical  machine  in  air  of  the  usual  density, 


486  NATURAL    PHILOSOPHY. 

the  light  is  intense  and  nearly  white.  If  the  electricity  is 
passed  through  a  glass  vessel  in  which  the  air  has  been  partially 
rarefied,  the  light  is  more  diffuse  and  inclines  to  a  delicate  rosy 
hue.  If  the  air  is  still  further  rarefied,  the  light  becomes  very 
diffuse,  and  its  color  becomes  a  deep  rose  or  purple.  The  same 
variety  of  colors  is  observed  during  the  aurora.  The  transition 
from  a  white  or  pale  straw  color  to  a  rosy  hue,  and  finally  to  a 
deep  red,  probably  depends  upon  the  height  above  the  earth, 
and  upon  the  amount  of  condensed  vapor  present  in  the  air. 

The  formation  of  an  auroral  corona  near  the  magnetic  zenith 
is  the  effect  of  perspective,  resulting  from  a  great  number  of 
luminous  beams  all  parallel  to  each  other.  A  collection  of  beams 
parallel  to  the  direction  of  the  clipping  needle  would  appear  to 
converge  towards  the  pole  of  the  needle,  and  no  other  supposi- 
tion will  explain  all  the  appearances  which  we  observe.  The 
auroral  crown,  therefore,  everywhere  appears  in  the  magnetic 
zenith,  and  it  is  not  the  same  crown  which  is  seen  at  different 
places  any  more  than  it  is  the  same  rainbow  which  is  seen  by 
different  observers. 

The  auroral  beams  are  simply  illumined  spaces  caused  by  the 
flow  of  electricity  through  the  upper  regions  of  the  atmosphere. 

The  slaty  appearance  of  the  sky  which  is  remarked  in  all 
great  auroral  exhibitions  arises  from  the  condensation  of  the 
vapor  of  the  air,  and  this  condensed  vapor  probably  exists  in 
the  form  of  minute  spiculas  of  ice  or  flakes  of  snow.  Fine 
flakes  of  snow  have  been  repeatedly  observed  to  fall  during  the 
exhibition  of  auroras,  and  this  snow  only  slightly  impairs 
the  transparency  of  the  atmosphere,  without  presenting  the 
appearance  of  clouds.  It  produces  a  turbid  appearance  of  the 
sky,  and  causes  that  dark  bank  which  in  the  United  States  rests 
on  the  northern  horizon.  This  turbidness  is  more  noticeable 
near  the  horizon  than  it  is  at  great  elevations,  because  near  the 
horizon  the  line  of  vision  traverses  a  greater  depth  of  this  hazy 
atmosphere.  When  the  aurora  covers  the  whole  heavens,  the 
entire  atmosphere  is  filled  with  this  haze,  and  a  dark  segment 
may  be  observed  resting  on  the  southern  horizon. 

The  vapor  which  arises  from  the  ocean  in  all  latitudes,  but 
most  abundantly  in  the  equatorial  regions  of  the  earth,  carries 
into  the  upper  regions  of  the  atmosphere  a  considerable  quantity 


NATURAL    PHILOSOPHY.  487 

of  positive  electricity,  while  the  negative  electricity  remains  in 
the  earth.  This  positive  electricity,  after  rising  nearly  vertically 
with  the  ascending  currents  of  the  atmosphere,  would  be  con- 
veyed towards  either  pole  by  the  upper  currents  of  the  atmos- 
phere. 

The  earth  and  the  rarefied  air  of  the  upper  atmosphere  may 
be  regarded  as  forming  the  two  conducting  plates  of  a  con- 
denser, which  are  separated  by  an  insulating  stratum,  namely,  the 
lower  portion  of  the  atmosphere.  The  two  opposite  electricities 
must  then  be  condensed  by  their  mutual  influence,  especially  in 
the  polar  regions,  where  they  approach  nearest  together,  and 
whenever  their  tension  reaches  a  certain  limit  there  will  be 
discharges  from  one  conductor  to  the  other.  When  the  air  is 
humid  it  becomes  a  partial  conductor,  and  conveys  a  portion  of 
the  electricity  of  the  atmosphere  to  the  earth.  On  account  of  the 
low  conducting  power  of  the  air,  the  neutralization  of  the  oppo- 
site electricities  would  not  be  effected  instantaneously,  but  by 
successive  discharges,  more  or  less  continuous  and  variable  in 
intensity.  These  discharges  should  frequently  occur  simulta- 
neously at  the  two  poles,  since  the  electric  tension  of  the  earth 
t  i},  4V,  should  be  nearly  the  sime  at  each  pole. 

Figure  498  represents  the  system  of 
circulation  here  supposed,  the  north  and 
south  poles  of  the  earth  being  denoted  by 
the  letters  A' and  S. 

When  electricity  from  the  upper  re- 
gions of  the  atmosphere  discharges  it- 
self to  the  earth  through  an  imperfectly 
conducting  medium,  the  flow  cannot  be 
everywhere  uniform,  but  must  take  place 
chiefly  along  certain  lines  where  the  resistance  is  least :  and  this 
current  must  develop  light,  forming  thus  an  auroral  beam.  It 
might  be  expected  that  these  beams  would  have  a  vertical  posi- 
tion, but  their  position  is  controlled  by  the  earth's  magnetism. 
It  is  found  that  when  magnetic  forces  act  upon  a  perfectly  flexi- 
ble conductor  through  which  an  electric  current  passes,  the 
conductor  must  assume  the  form  of  a  magnetic  curve.  Now 
at  each  point  of  the  earth's  surface  the  dipping  needle  shows 
the  direction  of  the  magnetic  curve  which  passes  through  its 


488  NATURAL   PHILOSOPHY. 

base ;  and  since  adjacent  streamers  are  sensibly  parallel,  the 
beams  appear  to  converge  towards  the  magnetic  zenith. 

When  electricity  escapes  from  a  metallic  conductor  under  a 
receiver  from  which  the  air  has  been  exhausted,  and  this  con- 
ductor is  the  pole  of  a  powerful  magnet,  the  electric  light  forms 
a  complete  luminous  ring  around  it. 

In  like  manner,  the  auroral  arch  is  a  part  of  a  luminous  ring 
nearly  parallel  to  the  earth's  surface,  having  the  magnetic  pole 
for  its  centre,  and  cutting  all  the  magnetic  meridians  at  right 
angles  ;  and  this  position  results  from  the  influence  of  the  earth's 
magnetism. 

The  flashes  of  light  observed  in  great  auroral  displays  are 
due  to  inequalities  in  the  motion  of  the  electric  currents.  On 
account  of  the  imperfect  conducting  power  of  the  air  the  flow  of 
electricity  is  not  perfectly  uniform,  but  escapes  by  paroxysms. 
The  flashes  of  the  aurora  are  therefore  feeble  flashes  of  light- 
ning. 

The  three  phenomena  —  solar  spots,  mean  daily  range  of  the 
magnetic  needle,  and  frequency  of  auroras  — exhibit  two  distinct 
periods :  one  a  period  of  from  ten  to  twelve  years,  the  other 
a  period  of  from  fifty-eight  to  sixty  years.  The  first  of  these 
periods  corresponds  to  one  revolution  of  Jupiter,  and  the  sec- 
ond to  five  revolutions  of  Jupiter  or  two  of  Saturn  ;  and  we  can 
scarcely  doubt  that  the  phenomena  depend  upon  the  movements 
of  these  planets.  Observations  have  also  indicated  subordinate 
fluctuations,  which  are  probably  due  to  the  action  of  Venus. 

We  do  not  know  how  the  planets  exert  an  influence  upon  the 
sun's  surface,  but  we  may  suppose  that  there  are  circulating 
round  the  sun  powerful  electric  currents,  which  may  possibly  be 
the  source  of  the  sun's  light;  these  currents  may  act  upon  the 
planets,  developing  in  them  electric  currents,  and  the  currents 
circulating  round  the  planets  may  react  upon  the  solar  cur- 
rents with  a  force  varying  with  their  distances  and  relative 
positions,  exhibiting  periods  corresponding  to  the  times  of 
revolution  of  the  planets.  These  disturbances  of  the  solar  cur- 
rents may  be  one  cause  of  the  solar  spots,  and  an  unusual  dis- 
turbance of  the  solar  currents  may  cause  a  disturbance  of  the 
currents  of  the  earth's  surface,  giving  rise  to  unusual  displays 
of  the  aurora. 


NATURAL   PHILOSOPHY.  489 

The  geographical  distribution  of  auroras  depends  chiefly 
upon  the  relative  intensity  of  the  earth's  magnetism  in  different 
latitudes.  According  to  experiments  with  artificial  magnets, 
the  electric  light  tends  to  form  a  ring  around  the  pole,  and  at 
some  distance  from  it.  The  electric  light  should  therefore  be 
most  noticeable  in  the  neighborhood  of  the  earth's  magnetic 
pole,  but  not  directly  over  it.  Auroras  are,  accordingly,  most 
abundant  along  a  certain  zone  which  follows  nearly  a  magnetic 
parallel,  being  everywhere  nearly  at  right  angles  to  the  mag- 
netic meridian  of  the  place. 

The  electricity  of  the  tropical  regions  has  great  intensity,  and 
moves  with  explosive  violence  in  thunder-showers,  while  the 
magnetic  intensity  in  those  regions  is  very  feeble,  and  is  not 
sufficient  to  control  the  movements  of  the  electricity.  In  the 
higher  latitudes  thunder-showers  become  infrequent,  the  elec- 
tricity of  the  atmosphere  passes  to  the  earth  in  a  slow  and  quiet 
manner,  and  these  discharges  are  controlled  by  the  magnetism 
of  the  earth. 

We  cannot  explain  the  great  auroral  displays  in  the  northern 
hemisphere  by  supposing  that  the  electricity  of  the  atmosphere 
is  temporarily  diverted  from  one  hemisphere  to  the  other,  for  the 
mean  range  of  the  magnetic  needle  exhibits  its  maxima  simul- 
taneously in  both  hemispheres;  neither  can  we  suppose  that 
the  absolute  amount  of  electricity  for  the  entire  globe,  as  devel- 
oped by  evaporation  from  the  water  of  the  ocean,  undergoes 
great  periodical  variations,  for  the  mean  temperature  of  the 
earth's  surface  does  not  change  sensibly  from  one  year  to 
another.  We  seem,  therefore,  compelled  to  ascribe  these  great 
auroral  displays  in  no  small  degree  to  the  direct  action  of  the 
sun,  through  the  agency,  perhaps,  of  its  magnetism,  or  of  the 
electric  currents  circulating  around  it.  Such  an  effect  should 
take  place  simultaneously  in  both  hemispheres. 


490 


NATURAL   PHILOSOPHY. 


VII. 

OPTICAL   PHENOMENA   OF   THE   ATMOSPHERE. 
A.  REFRACTION. 

583.  Astronomical  Refraction.  —  When  a  ray  of  light  from 
a  star  or  other  heavenly  body  enters  the  atmosphere  ob- 
liquely, it  will  be  bent  downward,  or  towards  a  vertical  line 
drawn  from  the  point  of  contact  of  the  ray  with  the  atmos- 

Fig.  499. 


phere  to  the  surface  of  the  earth  ;  and  as  the  atmosphere 
grows  denser  as  we  approach  the  earth,  the  ray  will  be 
bent  more  and  more  as  it  passes  through  the  atmosphere 
from  layer  to  layer.  As  we  always  see  the  body  which 
emits  the  ray  in  the  direction  of  the  ray  when  it  enters  the 
eye,  the  effect  of  this  refraction  will  be  to  make  every 
heavenly  body  appear  farther  above  the  horizon  and 
nearer  the  zenith  than  it  really  is.  A  star  in  the  zenith  is 
not  displaced  by  refraction,  because  the  rays  from  it  enter 


NATURAL    PHILOSOPHY. 


491 


the  air  perpendicularly,  and  therefore  without  bending. 
The  farther  a  star  is  from  the  zenith,  the  more  obliquely 
its  rays  enter  the  atmosphere,  and  the  greater  the  re- 
fraction. 

584.  Mirage.  —  Objects    within    the    atmosphere     are 
sometimes  displaced  or   made  to    appear  double    by  the 
refraction  of  the  air.     The  change  in  the  appearance  of 
objects  within  our  atmosphere  due  to  atmospheric  refrac- 
tion, is  called  mirage. 

585.  Mirage  upon  a  Desert.  —  Upon  a  hot  desert,  on  a 
still  clay,  objects  are  often  seen  reflected  in  a  lower  stratum 
of  air  so  as  to  give  the  appearance  of  water  (Figure  499). 

Fig.  500. 


The  layers  of  air  near  the  hot  sand  become  more  heated, 
and  consequently  rarer,  than  those  higher  up.  Hence  rays 
coming  from  any  object,  as  the  tree  (Figure  500),  would, 
on  passing  downward,  be  entering  continually  rarer  and 
rarer  layers  of  air.  They  would  therefore  be  bent  up- 
ward more  and  more,  till  they  finally  meet  a  layer  at  an 
angle  exceeding  the  limiting  angle,  and  become  totally 
reflected.  This  total  reflection  of  the  rays  causes  objects  to 
be  mirrored  in  the  layers  of  air  as  in  the  surface  of  water. 

586.  Mirage  over  Water.  —  Objects  at  a  distance  over 
water,  partially  or  entirely  below  the  horizon,  often  appear 
suspended  in  the  air,  sometimes  erect,  sometimes  inverted, 


492 


NATURAL  PHILOSOPHY. 


and  sometimes  both  erect  and  inverted,  as  shown  in  Figure 
Fig.  501.       501.     In  this  case  the  layers  of  air  near  the 
cold  surface  of  the   water  are  considerably 

Fig.  502. 


colder  and  denser  than  those  higher  up.  Rays,  therefore, 
which  pass  upward  from  an  object  are  continually  enter- 
ing rarer  layers  of  air,  and  are  therefore  bent  more  and 
more  downward,  as  shown  in  Figure  502.  If  the  rays 
A  C  and  B  D,  coming  from  the  top  and  bottom  of  the 
object,  are  totally  reflected  at  the  points  C  and  Z>,  they 
will  cross  on  their  way  to  the  eye,  and  cause  the  object  to 
appear  elevated  and  inverted  at  A '£'.  If  the  rays  com- 
ing from  the  top  and  bottom  of  the  object  are  simply  bent 
round  without  being  totally  reflected,  they  will  not  cross 
before  entering  the  eye,  and  the  object  will  appear  elevated 
and  erect,  as  at  A"B".  The  elevation  of  an  object  by 
refraction  without  inversion  is  sometimes  called  looming. 
Sometimes  objects  entirely  below  the  horizon  are  elevated  by 
refraction  sufficiently  to  appear  distinctly  above  the  horizon. 
587.  Lateral  Mirage. — Some- 
times vertical  layers  of  air  near 
a  shaded  bank  will  be  much 
colder  and  denser  than  layers 
farther  out  which  are  exposed 
to  the  sun.  This  gives  rise  to 
a  lateral  mirage,  similar  to  that 
over  the  water.  An  observer 
at  B  (Figure  503)  would  in  this  case  see  the  vessels  C  and 


Fig.  S°3. 


NATURAL   PHILOSOPHY.  493 

D  reflected  at  C  and  Z>,  as  in  the  surface  of  a  vertical 
mirror.  Sometimes  near  a  hot  well  there  occurs  a  case  of 
lateral  mirage  similar  to  the  mirage  over  a  desert. 

588.  The  Rainbow.  —  The  rainbow,  when  complete,  is  a 
colored  arc  having  a  radius  of  about  41°,  and  containing 
all  the  prismatic  hues,  the  red  being  on  the  outside  of  the 
arc  and  the  violet  on  the  inside.     There  is  often  a  second 
fainter  bow,  with  its  colors  in  the  reverse  order,  outside 
of  the   primary  bow.     This  is   called  the  secondary  bow. 
Occasionally,  there  are  one  or  more  supernumerary  bows 
within   the  primary   bow,  composed   of   colored   arcs    of 
greater  or  less  extent. 

The  rainbow  appears  whenever  the  sun  shines  upon 
falling  rain  in  the  opposite  part  of  the  heavens.  The  bow 
is  never  seen  unless  the  sun  is  within  41°  of  the  horizon, 
and  the  nearer  the  sun  is  to  the  horizon  the  larger  the  arc 
of  the  bow. 

A  line  drawn  from  the  sun  through  the  eye  of  the  ob- 
server points  to  the  centre  of  the  circle  of  which  the  rain- 
bow is  a  part,  and  is  called  the  axis  of  the  bow.  A  line 
drawn  from  the  eye  of  the  observer  to  the  centre  of  the 
colored  band  at  any  point  makes  an  angle  of  about  41° 
with  the  axis  of  the  bow.  A  line  drawn  from  the  eye  of  the 
observer  to  the  red  edge  of  the  bow  makes  an  angle  of 
about- 42^°  with  this  axis;  and  one  drawn  to  the  violet 
edge,  an  angle  of  about  40^°. 

When  the  sun  is  on  the  horizon,  the  centre  point  of  the 
bow  will  also  be  on  the  horizon  opposite  the  sun,  and 
the  middle  point  of  the  arc  will  be  41°  above  the  horizon. 
When  the  sun  is  above  the  horizon,  the  centre  of  the  bow 
will  be  below  the  horizon,  and  the  middle  point  of  the  arc 
nearer  the  horizon.  When  the  sun  is  41°  above  the  hori- 
zon, the  centre  of  the  bow  will  be  41°  below  the  horizon, 
and  the  middle  of  the  arc  on  the  horizon. 

589.  Explanation  of  the  Rainbow.  —  The  rainbow  is   pro- 


494 


NATURAL    PHILOSOPHY. 


Fig.  504. 


duced  by  rays  of  sunlight  reflected  from  the  rear  surface  of  the 
rain-drops.  These  rays  would  be  refracted  both  on  entering 
and  leaving  the  drops.  At  each  refraction  they  would  be  bent 
towards  a  line  drawn  to  the  point  of  contact  of  the  ray  with  the 
rear  surface  of  the  drop,  and  parallel  with  the  incident  ray  of 
sunlight,  and  therefore  parallel  with  the  axis  of  the  bow  (Figure 
504).  If  we  trace  the  path  of  every 
ray  of  sunlight  through  a  rain-drop 
according  to  Snell'slawof  refraction, 
we  shall  find  that  at  an  angle  of  41° 
with  the  axis  of  the  bow  the  rays 
emerge  from  the  rain-drop  crowded 
together  and  almost  parallel  with 
each  other  (Figure  505).  These  rays 
are  able  to  preserve  their  intensity  through  long  atmospheric 
distances.  At  all  other  angles  the  emergent  rays  are  divergent, 
and  through  their  divergence  they  become  too  feeble  to  affect 

Fig-  5°5- 


the  eye.  Accordingly,  whenever  the  observer  looks  41°  away 
from  the  axis  of  the  bow,  his  eye  catches  some  of  these  nearly 
parallel  rays  which  are  emerging  from  some  rain-drop.  He 
therefore  sees  a  bright  band,  circular  in  form,  and  having  a 
radius  of  41°. 

The  different  colored  rays  are  refracted  unequally  on  their 


NATURAL    PHILOSOPHY. 


496 


passage  through  the  rain-drop  ;  hence  the  angle  of  parallelism  is 
somewhat  different  for  different  colors,  being  about  42^°  for  the 
red  and  about  40%°  for  the  violet.  This  accounts  for  the  colors 
of  the  rainbow,  the  violet  rays  reaching  the  eye  from  drops 
nearer  the  axis  than  those  which  send  red  rays  to  the  eye.  No 

Fig.  506. 


two  observers  see  the  same  rainbow ;  that  is  to  say,  no  two  eyes 
receive  the  colors  from  the  same  set  of  rain-drops. 

The  secondary  bow  is  produced  by  rays  that  have  suffered 


Fig-  507- 


two  reflections  within  the  rain- 
drops (Figure  506).  Figure 
507  shows  the  relative  posi- 
tion of  the  two  bows. 

The  supernumerary  bows 
are  due  to  the  interference  of 
rays  which  emerge  from  rain- 
drops in  nearly  the  same  di- 
rection after  having  suffered 
different  degrees  of  retarda- 
tion, so  as  to  bring  their  waves 
into  opposite  phases.  One  of 
these  rays  suffers  more  re- 
tardation within  the  rain-drop 
than  another,  because  it  has  a 
longer  path  within  the  drops.  As  a  rule,  rays  of  light  are 
retarded  in  traversing  a  denser  medium. 


49^  NATURAL   PHILOSOPHY. 

B.   REFLECTION. 

590.  Diffused  Daylight.  —  When   the  sun  shines  upon 
any  portion  of  the  atmosphere,  the  particles  of  air  reflect 
the  rays  of  light  irregularly,  and  so   scatter  the  light  in 
every  direction,  thus  giving  rise  to  diffused  daylight.     Were 
it  not  for  the  atmosphere,  shadows  would  be  utterly  devoid 
of  light,  and  rooms  into  which  the  sun  was  not  directly 
shining  would  be  totally  dark. 

591.  Twilight. —  Were  it  not  for  the  atmosphere,  the 
darkness  of  midnight  would  begin  the  moment  the  sun 
sank  below  the  horizon,  and  would  continue  till  he  rose 
again  above  the  horizon  in  the  east,  when  the  darkness  of 
the  night  would  be  suddenly  succeeded  by  the  full  light  of 
day.     The  gradual  transition  from  the  light  of  day  to  the 
darkness  of  the  night,  and  from  the  darkness  of  the  night 
to  the  light  of  day,  is  called  twilight,  and  is  due  to  the  dif- 
fusion of  light  from  the  upper  layers  of  the  atmosphere 
after  the  sun  has  ceased  to  shine  on  the  lower  layers  at 
night,  or  before  it  has  begun  to  shine  upon  them  in  the 
morning. 

Twilight  begins  and  ends  when  the  sun   is  about   18° 
below  the  horizon. 

592.  Color  of  the  Sky.  — Large  particles  reflect  and  dif- 
fuse all  luminous  waves  equally  well,  but  a  particle  inter- 
mediate in  size  between  a  red  and  a  violet  wave  would 
reflect  a  greater  proportion  of  violet  waves  than  of  red 
waves.     The  smaller  the  particles  suspended  in  a  trans- 
parent medium,  the  greater  the  proportion  of   blue  rays 
reflected  and  the  less  the  proportion  of  red.     Hence  any 
transparent   medium    holding    very   minute    particles    of 
any  kind  in  suspension  will  appear  blue  in  reflected  light. 
According  to  Tyndall,  the  sky  owes  its  blue  color  to  the 
minute  particles  of  watery  vapor  or  other  substance  sus- 
pended in  it.    The  more  minute  the  particles,  the  bluer  the 


NATURAL    PHILOSOPHY. 


497 


sky.  As  we  approach  the  horizon  the  sky  inclines  to 
white,  because  of  the  larger  particles  which  are  present  in 
the  lower  layers  of  the  atmosphere. 

When  the  sun  is  near  the  horizon,  the  rays  traverse  a 
greater  atmospheric  distance,  and  the  separation  between 
the  long  and  short  waves  is  more  complete.  In  this  case 
the  rays  which  reach  us,  and  which  illumine  the  clouds  and 
the  lower  portion  of  the  sky,  are  those  which  are  allowed 
to  pass  the  particles,  and  not  those  which  are  reflected  by 
them.  Hence  the  evening  sky  inclines  to  yellow,  orange, 
or  red,  according  as  the  shorter  waves  have  been  more  or 
less  completely  turned  back.  Unless  there  are  clouds  in 
the  upper  portions  of  the  sky,  these  colors  are  limited  to 
the  regions  near  the  horizon,  since  it  is  there  only  that  the 
particles  in  the  air  are  large  enough  to  reflect  the  larger 
waves  transmitted  to  them. 

C.     CORONJE   AND    HALOS. 

593.  Corona.  —  When  light  fleecy  clouds  pass  over  the 
sun  or  moon,  one  or  more  iris-colored  rings  are  often  seen 
about  these  bodies,  the  inner  ring  being  from  3°  to  6°  in 
diameter.     The  blue  edges  of  these  rings  are  towards  the 
sun  or  moon,  and  the  red  edges  away  from  it.    These  rings 
are    called   corona.      They   are   more   frequently   noticed 
about  the  moon  than  about  the  sun,  owing  to  the  dazzling 
brilliancy  of  the  latter.     They  are  caused  by  the  diffraction 
of  the  rays  of  light  as  they  pass  through  the  small  spaces 
between  the  particles  of  the  cloud.     They  are  shown  at  the 
centre  of  the  lower  part  of  Figure  508. 

594.  Halos.  —  Halos  are  circles  formed  around  the  sun 
or  moon.     When  bright  they  are  seen  to  be  composed  of 
the  prismatic  colors.      They  are  larger  than  coronas,  and 
are  red  on  the  edge  towards  the  sun.     The  halo  most  often 
seen  has  a   radius  of  22°.     This  is  shown  at  hh  (Fig- 
ure 508).     A  second  halo  is  sometimes  formed  having  a 


498  NATURAL    PHILOSOPHY. 

radius  of  46°,  H H ;  and  occasionally  a  third  halo  is  seen 
having  a  radius  of  about  90°,  H'  H' .  These  halos  are 
formed  by  the  refraction  of  the  rays  of  light  on  their 
passage  through  crystals  of  ice  floating  in  the  atmos- 
phere. Even  in  midsummer,  at  a  moderate  elevation  above 
the  surface  of  the  earth,  the  condensed  vapor  is  frozen. 
These  ice  crystals  may  be  numerous  enough  to  form  circles 
about  the  sun  and  moon  without  giving  the  appearance  of 


a  cloud.  When  present  they  impart  a  greater  or  less  de- 
gree of  haziness  to  the  atmosphere.  The  simplest  form  of 
an  ice  crystal  is  a  right  prism,  whose  section  is  a  regular 
hexagon,  and  whose  sides  are  perpendicular  to  its  base. 
The  alternate  sides  of  such  a  prism  are  inclined  to  each 
other  at  an  angle  of  60°. 

The  halo  having  a  radius  of  22°  is  formed  by  the  refrac- 
tion of  the  rays  of  light  which  pass  through  the  alternate 
sides  of  the  prism  ;  and  the  halo  of  46°,  by  the  refraction 


NATURAL    PHILOSOPHY.  499 

of  the  rays  passing  through  one  side  and  the  adjacent  base. 
The  halo  of  90°  appears  to  be  formed  by  rays  which  suffer 
one  internal  reflection  on  passing  through  the  crystal. 

595.  Parhelic  Circle.  —  "  When  a  halo  is  formed  around 
the  sun  we  often  notice  a  white  circle  passing  through  the 
sun   and  parallel   to  the  horizon    (Figure  508).     This  is 
called  z.  parhelic  circle,  and  is  produced  by  the  reflection  of 
the  sun's  light  from  ice  prisms  or  snow  crystals  whose  sur- 
faces have  a  vertical  position.    When  the  air  is  tranquil,  the 
flakes  of  snow  which  are  present  in  the  atmosphere  descend 
slowly  to  the  earth,  and  they  tend  to  assume  that  position 
in  which  they  experience  the  least  resistance  from  the  air. 
For  most  forms  of  snow-flakes,  this  position  will  be  when 
the  principal  faces  of  the  crystal  are  perpendicular  to  the 
horizon,  and  the  light  of  the  sun  may  reach  the  eye  reflected 
from  such  snow-flakes  as  are  situated  on  a  horizontal  circle 
passing  through  the  sun.     This  circle  never  exhibits  pris- 
matic colors  like  the  first-mentioned  halos." 

596.  Parhelia.  — "  Near  those  points  where  halos  cut 
the  parhelic  circle  there  is  a  double  cause  of  light,  and  here 
the  illumination  is  sometimes  so  great  as  to  present  the 
appearance  of  a  mock  sun,//  and  P P  (Figure  508),  and 
is  called  &  parhelion. 

"  Parhelia  are  generally  red  on  the  side  which  is  toward 
the  sun,  and  they  sometimes  have  a  prolongation  i:i  t lie- 
form  of  a  tail  several  degrees  in  length,  whose  direction 
coincides  with  that  of  the  horizontal  circle." 

597.  Contact  Arches.  —  "Arcs   of  colored  circles  with 
variable  curvatures  are  sometimes  seen  touching  the  halos 
of  22°  and  46°  at  their  highest  and  lowest  points,  a,  l>  (  Ki» 
ure  508).     These  are  due  to  the   refraction   of  the  sun's 
light  through  ice  prisms,  some  of  them   having  their  axes 
perpendicular  to  the  sun's  rays,  and    others   inclined   at 
various  angles,  but  all  in  a  horizontal  position.     The  sun's 
light,  refracted  by  such  prisms  as  have  their  axes  not  only 


500  NATURAL   PHILOSOPHY. 

horizontal,  but  perpendicular  to  the  solar  rays,  will  produce 
a  bright  image  directly  over  or  under  the  sun.  But  the  sun's 
light,  passing  through  prisms  whose  axes  are  inclined  to 
the  solar  rays,  will  experience  a  greater  deviation,  and  also 
a  deflection  from  a  vertical  plane.  Thus,  if  we  look  at 
a  long  straight  bar  through  a  prism  whose  axis  is  parallel 
to  the  bar,  the  straight  bar  appears  curved,  the  deviation 
being  greatest  in  the  case  of  those  rays  which  are  oblique 
to  the  axis  of  the  prism." 

"  Sometimes  we  notice  two  arcs  of  circles  nearly  white, 
A  (Figure  508),  intersecting  the  parhelic  circle  at  a  point 
directly  opposite  to  the  sun,  and  inclined  to  this  circle  at 
angles  of  about  60°. 

"  They  are  probably  due  to  reflection  from  surfaces  ob- 
lique to  the  horizon." 

598.  Vertical  Columns  passing  through  the  Sun.  —  "  Some- 
times, near  sunset,  we  notice  a  luminous  column,  perpen- 
dicular to  the  horizon,  rising  from  the  sun  to  a  height  of 
10°  or  15°,  and  occasionally  still  higher.  This  column  is  due 
to  the  reflection  of  the  sun's  light  from  the  under  faces  of 
ice  crystals,  which  are  nearly  parallel  to  the  horizon.  Some- 
times, a  little  before  sunset,  a  similar  column  of  light  is  seen 
to  shoot  down  from  the  sun  toward  the  horizon.  This  is 
formed  in  a  similar  manner  by  rays  of  the  sun  reflected 
from  the  upper  faces  of  crystals  in  a  nearly  horizontal  posi- 
tion. Sometimes  columns  are  seen  simultaneously  both 
above  and  below  the  sun  ;  and  if  the  halo  of  22°  is  seen 
at  the  same  time,  this  column,  together  with  the  parhelic 
circle,  presents  the  appearance  of  a  rectangular  cross 
within  the  halo  (Figure  508).  These  luminous  columns 
are  probably  formed  only  when  the  air  is  very  tranquil, 
and  the  reflecting  surfaces  may  be  the  rectangular  termi- 
nations of  spicuke  of  ice,  which  are  slowly  falling  to  the 
earth  with  their  axes  nearly  in  a  vertical  position. 

"  When  we  remember  the  immense  variety  in  the  forms 


NATURAL   PHILOSOPHY.  501 

of  snow-flakes,  a  few  of  which  are  represented  in  Fig- 
ure 486,  we  should  anticipate  a  very  great  variety  in  the 
figures  which  might  be  produced  from  the  refraction  or  re- 
flection by  them  of  the  sun's  light." 


VIII. 

THE  THREE   GREAT  CIRCULATIONS   OF   THE 
GLOBE. 

599.  The  Atmospheric  Circulation.  —  In  the  atmospheric 
circulation,  which   gives   rise  to  the   various    systems   of 
winds,  masses  of  air  are  kept  moving  round  and  round 
This  circulation  is  maintained  by  heat  received  from  the 
sun,  and  absorbed  by  the  atmosphere.     The  heat  thus  ab- 
sorbed causes  the  air  to  expand,  rise,  and  overflow,  while 
gravity  pulls  the  colder  and  heavier  air  down  and  around 
to  supply  its  place.    The  mechanical  energy  of  the  moving 
masses  of  air  is  exactly  equal  to  the  energy  of  the  solar 
radiations  consumed  in  maintaining  the  motion.     The  en- 
ergy of  the  solar  radiations  absorbed  by  the  air  is  trans- 
formed by  expansion  into  the   mechanical  energy  of  the 
winds.     Winds  are  merely  transmuted  sunshine. 

600.  The  Aqueous  Circulation.  —  In  the  aqueous  circu- 
lation, water  is  continually  passing  into  the  atmosphere 
as  vapor,  then  falling  from  the  atmosphere  as  rain,  and, 
finally,  running  in  various  streams  down  to  the  level  of  the 
ocean.     This  circulation  is  also  maintained  by  energy  ab- 
sorbed from  solar  radiations.     The  solar  heat  absorbed  by 
water  converts  it  into  vapor,  and  raises  it  into  the  atmos- 
phere.    When  this  vapor  condenses  in  the  atmosphere, 
gravity  draws  it  to  the  surface  of  the  earth,  and  to  the  level 
of  the  ocean.     In  the  evaporation  of  the  water  the  kinetic 
energy  of  the  solar  radiations  is  converted  into  the  potential 
energy  of  molecular  separation,  and  in  the  expansion  by 


5<D2  NATURAL   PHILOSOPHY. 

which  this  vapor  is  raised  into  the  atmosphere,  into  the  po 
tential  energy  of  mechanical  separation.  In  the  condensa 
tion  of  the  vapor  in  the  atmosphere,  its  potential  energy  of 
molecular  separation  is  transformed  into  the  kinetic  energy  of 
heat,  and  in  the  fall  of  the  rain  to  the  earth  and  the  descent 
of  the  water  to  the  sea,  its  potential  energy  of  mechanical 
separation  is  transformed  into  the  kinetic  energy  of  me- 
chanical motion.  The  energy  of  the  mountain  stream 
which  drives  the  mill  came  originally  to  the  earth  in  the 
minute  vibrations  of  the  solar  radiations,  and  was  absorbed 
from  these  by  water  and  air. 

60 1.  The  Circulation  of  Carbon.  —  Carbon  exists  in  the 
atmosphere  in  carbonic  acid  gas,  a  compound  of  carbon 
and  oxygen.  This  gas  is  absorbed  from  the  atmosphere 
by  leaves  of  plants,  in  which  it  is  decomposed  by  solar 
radiations,  which  are  also  absorbed  by  the  leaves.  The 
carbon  is  retained  by  the  plant,  and  the  oxygen  is  restored 
to  the  atmosphere.  When  vegetable  substances  are  con- 
sumed by  the  natural  process  of  decay,  or  as  food  in  the 
bodies  of  animals,  or  as  fuel  in  our  stoves  and  furnaces, 
the  carbon  again  unites  with  the  oxygen  and  forms  car- 
bonic acid,  which  passes  back  into  the  atmosphere.  Thus 
carbon  is  kept  going  round  and  round,  from  the  atmos- 
phere to  plants  and  animals,  and  back  again  into  the  atmos- 
phere. This  circulation,  like  the  other  two,  is  maintained 
by  energy  obtained  from  solar  radiation.  By  the  decom- 
position of  the  carbonic  acid  in  the  leaves  of  the  plant,  the 
kinetic  energy  of  the  sunbeam  is  transformed  into  the  po- 
tential energy  of  chemical  separation  ;  and  in  the  con- 
sumption of  food  and  fuel,  the  potential  energy  thus 
required  by  carbon  is  converted  into  kinetic  energy  again. 
Animals  derive  all  their  energy  from  the  food  which  they 
eat,  and  as  this  food  is  consumed  in  the  body,  its  potential 
energy  is  converted  partly  into  the  kinetic  energy  of  heat, 
and  partly  into  the  kinetic  energy  of  mechanical  motion. 


NATURAL  PHILOSOPHY.  503 

The  energy  employed  by  man  in  thinking,  writing,  speak- 
ing, or  in  doing  any  kind  of  work  whatever,  came  to  the 
earth  originally  from  the  sun  in  the  minute  vibrations  of 
the  ether. 

Coal  is  a  vegetable  substance,  and  its  potential  energy 
has  been  derived  from  solar  radiations,  and  when  we  burn 
coal  for  fuel  or  coal  gas  for  light,  we  are  simply  extracting 
from  the  coal  the  sunbeams  that  were  ages  ago  absorbed 
by  the  leaves  of  plants  and  transformed  into  the  potential 
energy  of  chemical  separation. 

602.  Source  of  Terrestrial  Energy.  —  Nearly  every  form 
of  terrestrial  energy  is  derived  from  the  sun  and  comes  to 
the  earth  in  the  solar  radiations.  The  three  chief  agents 
for  absorbing  this  energy  and  transforming  it  into  a  kind 
adapted  for  our  use  are  water,  air,  and  leaves  of  plants. 


INDEX. 


Aberration  chromatic,  340. 
spherical,  240. 
Actinophone,  the,  282. 
Action  and  reaction,  12. 
Air-chamber  in  pumps,  108. 
Air,  pressure  of,  83. 
Air-pump,  the,  85. 

Sprengel's,  87. 
Ampert's  rule,  335. 
Anion,  the,  357. 
Anode,  the,  357. 
Aqueous  circulation,  the,  501. 
Archimedes's  principle,  75. 
Artesian  wells,  96. 
Astatic  galvanometer,  336. 

needle,  336. 
Astronomy,  8 
Atmosphere,  circulatjon  in,  501. 

composition  of,  430. 

condensation  in,  455. 

electricity  in,  475. 

height  of,  430. 

humidity  of,  443. 

reflection  in,  496. 

refraction  in,  41/0. 

temperature  of,  434. 

weight  of,  431. 
Atoms,  3. 

Audiometer,  the,  372. 
Aurora,  the,  481. 

theory  of,  485. 


B. 

Balance,  the,  40. 

induction,  372s 

Balance-wheel,  compensation,  160. 
Ballimns,  77. 

Barometer,  the,  105,  431, 
Batteries,  secondary,  361. 
Beam,  defined,  207. 
Beats,  musical,  140. 
Bell's  telephone,  365. 
Boiling,  173. 
Brocken,  the  spectre  of  the,  356. 


Brush's  electric  lamp,  4 17. 
Bunsen's  cell,  350. 


Calorimeters,  181. 

Camera  obscura,  the,  248. 

Capillarity,  99. 

Capstan,  the,  65. 

Carbon,  circulation  of,  502. 

Cathode,  the,  357- 

Cation,  the,  35.7 

Centre  of  gravity,  34. 

Centrifugal  force,  14. 

Centripetal  force,  15. 

C.  G.  S.  system,  17. 

Chemistry,  8. 

Climates,  marine  and  continental,  440. 

Clocks,  52. 

Clouds,  460. 

Cog-wheels,  63. 

Cohesion,  70. 

Coil,  the  induction,  368. 

Collision  of  elastic  bodies,  23. 

Colloi.Is,    102. 

Color-blindness,  267. 
Color  chart,  the,  261. 

of  the  sky.  49^ 

perception,  265. 

scale,  262. 

theory  of.  260,  265. 
Color-disc,  the  ideal,  260. 
Colors,  from  absorption,  268. 

from  polarization,  273,  277. 
of  soap-bubbles,  269. 
primary,  262. 
Condensation,  176. 
Congelation,  170. 
C<mta<*Cirches,  499. 
Contact-breaker,  the,  376. 
Coronat   497. 

Cottrell  s  straw  electroscope,  299. 
Coulomb's  torsion  balance,  310. 
Crookes  on  radiant  matter,  418. 
Crown-wheels,  64. 
Cry"|'horiis  the,  186. 
Crystalloids,  102. 


5°6 


Crystals,  116. 
Cyclones,  473. 

Electro-motors,  409 
Electrophorus,  the,  301. 

Electroplating,  360. 

Electroscope,  Cottrell's,  299. 

D. 

gold-leaf,  302. 

Daniell's  cell,  351. 

Electro-statics,  334. 
Electro-thermal  action,  410. 

Daylight,  diffused,  496. 

Electrotyping,  359. 

Density,  10. 

Elliott  electrometer,  314. 

Dew,  origin  of,  455. 

Endosmose,  102. 

Dew-point,  the,  443. 

Energy,  denned,  27. 

Diamagnetic  bodies,  291. 

kinetic,  28. 

Diathermunous  bodies,  201. 

potential,  28. 

Dielectrics,  306. 
Diffraction  fringes,  270. 
Discharge,  auroral,  331. 

source  of  terrestrial,  503. 
Equilibrium,  36. 
of  floating  bodies,  78. 

brush,  332. 

Erg,  denned,  25. 

electrical,  327. 

Ether,  the,  4,  205. 

glow,  332. 

Evaporation,  172. 

spark,  329. 

latent  heat  of,  173. 

Distillation,  177. 
Dyne,  denned,  17. 

Exosmose,  102. 
Expansion,  latent  heat  of,  185. 

Extra  current,  the,  377. 

Eye,  the  human,  250. 

E. 

Eyes,  old,  259. 

Ear,  the  human,  154. 

Ear-trumpet,  the,  130. 

F. 

Ebullition,  173. 

Echoes,  128. 
Edison's  electric  lamp,  412. 

Falling  bodies,  42. 
Faraday's  liquefaction  of  pases,  189. 

machine,  383. 

nomenclature  of  electrolysis, 

phonograph,  152. 

3C7- 

telephone,  367. 

Far-sightedness,  258. 

Elasticity,  7. 
Electrical  attraction,  297,  307. 

Floating  bodies,  77. 
Fluids,  72. 

capacity,  320. 

Fluorescence,  277. 

charge,  314. 

Fog,  458. 

condensation,  321. 
conductors,  299. 

Foot-poundal,  denned,  24. 
Force,  defined,  it. 

discharge,  327. 

impulse  of,  18. 

excitation,  296 

units  of,  17. 

induction,  300. 
insulators,  300. 
machine,  318. 
potential,  308. 

Force-pump,  the,  108. 
Forces,  composition  of,  29. 
parallelogram  of,  30. 
resolution  of,  29.  34. 

repulsion,  298,  307. 

the  three  great,  u. 

resistance,  340. 

Foucatilt's  regulator,  416. 

Electric  carrier,  the,  303. 

Fountain  in  vacuo,  104. 

current,  334,  341- 

Franklin's  experiment,  175. 

illumination,  412. 

Freezing  mixtures,  187. 

mill,  319. 

Frost  in  valleys,  457. 

wind,  319 

Fnsing-point,  the,  169. 

Electricity,  atmospheric,  475. 

Fusion,  169. 

frictional,  296. 

latent  heat  of,  170. 

thermal,  410. 

two  kinds  of,  298. 

velocity  of,  346. 

G. 

voltaic,  334,  346. 

Electro-dynamics,  334. 
Electro-kinetics,  334. 

Galvanometer,  the,  335. 
astatic,  336. 

Electrolysis,  ,56. 

differential,  339. 

Electrolytic  polarization,  301. 
Electro-matrnetic  induction,  362, 

Thomson's,  337. 
Gases  and  vapors,  172. 

Electro-metallurgy,  359. 

conductivity  of.  198. 

Electro-majrnets,  362 
Electrometers,  310. 

critical  tenxperature  of,  190. 
diffusion  of;  83 

Electromotive  force,  339. 

expansibility  of,  82. 

INDEX. 


507 


Gases,  expansion  of,  162. 

K 

laws  of,  -84, 

solidification  of,  188. 
Gold-leaf.  118. 

Kaleidoscope,  the,  2  16. 
Koenig's  mauoraetric  flames,  151. 

Graham's  pendulum,  160. 

Gramme  machine,  the,  378. 

Gravitauon  units,  17. 

L. 

Gravity,  7. 

centre  of,  34* 

Land  and  sea  breezes,  455. 

law  of,  34- 

Lantern  for  projection,  250. 

Grove's  cell,  350. 

Leclanche'  cell,  353. 

Lenses,  achromatic,  241. 

axes  and  foci  of,  23  1  . 

H. 

Hail,  467. 

forms  of,  229. 
images  formed  by,  237. 
magnifying  power  of,  239. 

Halos,  497. 

Lever,  the,  57. 

Harrison's  pendulum,  160. 

compound,  58. 

Heat,  absorption  of.  202 
and  radiant  matter,  428. 

Leyden  jar,  the,  323. 
Light,  diffraction  of,  270. 

and  work,  184. 

diffusion  of,  214- 

conduction  of,  194. 

dispersion  of,  223. 

consumed  in  evaporation,  186. 

double  refraction  of,  276- 

expansion,  185. 

polarization  of,  273. 

liquefaction,  185. 
convection  of,  197,  199. 
distribuiion  of,  194. 

radiation  of,  205. 
reflection  of,  214. 
refraction  of,  217. 

effects  of,  157- 

total  reflection  of,  219. 

expansion  by,  157. 

velocity  of,  206. 

latent,  170. 
measurement  of,  180. 

Lightning.  477- 
Lightning-rods,  478. 

mechanical  equivalent  of,  192. 
radiation  of,  199. 

Liquids,  compressibility  of,  90. 
conductivity  of,  197. 

specific,  180. 

efflux  of.  in. 

unit  of,  180. 

evaporation  of,  172. 

Hoar-frost,  457. 

expansion  of,  161. 

Holtz's  electrical  machine,  327. 

pressure  of,  92. 

Hot-houses,  204. 

volatile,  172. 

Hydraulic  press,  the,  73. 

Lodestone,  the,  285. 

tourniquet,  the,  114. 

Hydrometers,  81. 

Hygrometer,  the,  442. 
Mason's,  443- 

M. 

Hypsometer,  the,  175. 

Machines,  53. 

I. 

Magdeburg  hemispheres,  88. 
Magnetic  action  on  radiant  matter,  427. 
force,  lines  of,  286. 

Ice,  manufacture  of,  187. 
Illumination,  212 

induction,  288. 
needles,  291,334. 

Inclined  plane,  the,  66. 
Indian  summer.  460. 
Induction  balance.  372. 
coils,  368,  375. 
Inertia,  12. 
I  ngenhousz's  experiment,  196. 
Images,  formed  by  lenses,  237. 
from  small  apertures,  207. 
in  concave  mirrors,  242. 
in  convex  mirrors,  243. 
in  plane  mirrors,  214. 
multiple,  215- 
Ions,  357. 

storms,  294. 
Magnetism,  2^5. 
terrestrial,  292. 
Magnetization  of  steel  bars,  289. 
Magnets,  283. 
Magneto-electric  currents,  363. 
machines,  378. 
Malus's  polariscope,  275. 
Mariner's  compass,  the,  295. 
Mariotte's  law,  84. 
Mason's  hygrometer,  443. 
Matter,  constitution  of,  3. 
properties  of,  7. 
radiant,  418. 

Irradiation,  254. 

three  states  of,  70. 

Mechanical  powers,  54. 

T 

Melting-point,  the.  i6q. 

J. 

Metals,  conductivity  of,  197. 

Joule's  method,  192. 

Meteorology.  430. 

5°8 


Metre,  the,  9. 

Prisms,  achromatic,  224. 

Metric  system,  the,  9. 

direct-vision,  224. 

Microphone,  the,  370. 
Microscope,  simple,  243. 

rectangular,  220. 
Proof-plane,  the,  303. 

compound,  243. 

Pyrometers,  167. 

Mirage,  491. 

Pulley,  the,  60. 

Mirrors,  concave,  241. 

convex,  243. 

plane,  214. 

R. 

Mist,  459. 
Molecules,  3,  70. 

Radiant  matter,  418. 

Momentum,  iS,,  25. 
Motion,  atomic,  6. 

Radiation,  theory  of,  228. 
Radiations,  luminous,  201. 

molar,  6. 

obscure,  201. 

molecular,  6. 

Radiometer,  the.  429. 

parallelogram  of,  22. 
produced  by  radiant  matter,  426. 
Musical  instruments,  144. 

Radiophone,  the,  279. 
Rain,  origin  of,  464. 
Rainbow,  the,  493. 

Ray,  defined,  20;. 

Reaction,  12. 

N. 

Reflection,  total,  219. 

Refraction,  law  of,  219. 

Natural  philosophy,  8. 
Near-sightedness,  257. 
Newton's  first  law  of  motion,  12. 

Relay,  the,  386. 
Resistance  boxes,  341. 
coils,  341. 

second  law  of  motion,  18. 

-Resonance,  141. 

third  law  of  motion,  22. 

Resonators,  150. 

Nickel-plating,  361. 

Rumford's  photometer,  214. 

Nodal  lines,  121. 

Noise,  133. 

S. 

0. 

Screw,  the,  68. 

endless,  69. 

Ohm,  the,  341. 

Shadows,  210. 

Opaque  bodies,  211. 

Siemens  machine,  the,  380. 

Opera-glass,  the,  246. 
Optical  axis,  the,  254. 

Singing  flames,  148. 
Siphon,  the,  109. 

Organ  pipes,  145. 

Siphon  recorder,  the,  406. 

Siren,  the,  133. 

Smee's  cell,  349. 

P. 

Snow  crystals,  466. 

line  of  perpetual,  441. 

Papin's  digester,  176. 

origin  of,  466. 

Parachute,  the,  78. 

Soap-bubbles,  colors  of,  269. 

Paramagnetic  bodies,  291. 

Solids,  crystalline,  116. 

Parhelia,  499. 
Parhelic  circle,  499. 

expansion  of,  157. 
properties  of,  118. 

Pascal's  experiment,  105. 

Sonometer,  the,  144. 

law,  72. 

Sound,  analysis  of,  149. 

vases,  95. 

intensity  of,  127. 

Pendulum,  the,  49. 
Pendulums,  compensating,  159. 
Penumbra  of  shadow,  211. 

interference  of,  139. 
origin  of,  120 
pitch  of,  132. 

Phonograph,  the,  152. 

propagation  of,  124. 

Phosphorescence,  277,  422. 

quality  of,  133. 

Photometry,  213. 

radiant    energy    converted  into 

Pliotophone,  the,  282,  283. 

278. 

electrical    receiver  of   the, 

reflection  of,  128. 

refraction  of,  128. 

Physical  sciences,  the,  8. 

velocity  of,  127. 

Physics,  8. 
Po^e-changer,  the,  399. 
Pores,  6. 
Position  of  advantage,  28. 
Potential,  electrical,  308. 
gravitation,  308. 
Poundal,  defined,  17. 

waves,  125. 
Sounding-boards,  143. 
Spangled  pane,  the,  330 
Speaking-trumpet,  the,  130. 
Specific  gravity,  41,  79. 
Spectrophone,  the,  281. 
Spectroscope,  the,  225. 

5°9 


Spectrum  analysis,  227. 
bright-lined,  227. 

Units,  English,  9. 
French,  9. 

continuous,  227. 

gravitation,  17. 

diffraction,  272. 

material,  7. 

dispersion,  223. 

mechanical,  9. 

reversed,  227. 

of  force,  17. 

Spheroidal  state,  178. 

of  work,  24. 

Spirit-level,  the,  96. 

Spottiswoode's  induction  coil,  375. 

V. 

Springs,  96,  in. 

Spur-wheels,  64. 

Vapors,  172,  176. 

Stability  of  rotation,  16. 

Varley's   method  of  submarine  telegra- 

Steam-engine, the,  194. 
Steam,  latent  he.it  of,  183. 

phy,  407. 
Velocity,  n. 

>pe,  the,  256. 

Vena  contracta,  the,  113. 

Storms,  469. 

Vibrations,  fundamental,  121. 

Strain,  defined,  7. 

harmonic,  124. 

Stress,  defined,  7,  11. 
Stringed  instruments,  144. 
Substance,  3. 

sympathetic,  141. 
Visual  angle,  the,  254. 
Voice,  the  human,  148. 

Suction-pump,  the,  107. 

Voltaic  battery,  the,  353. 

arc,  the,  414.' 

cell,  the,  346. 

T. 

bichromate  of  potash,  350. 

Tantalus's  cup,  1  10. 
Telegraph  key,  the,  384. 

Bunsen's,  350. 
Daniell's,  351. 

Morse's,  383. 

gravity,  352. 

register,  386. 
relay,  386. 
sounder,  3*5. 
terminal  stations,  388. 
way  station,  396 
Telegraphy,  duplex,  392. 
quadruplex,  399. 

Grove  s,  350. 
Leclanche',  353. 
Smee's,  349. 
Thomson's  tray,  332. 
zinc  and  copper,  348. 
cells,  two-fluid,  350. 
Vortex  theory  of  atoms,  4. 

submarine,  404. 

duplex,  408. 

VV. 

Telephone,  Bell's,  365. 
Edison's,  367. 
Telescope,  the,  244- 
reflecting,  246. 
terrestrial,  246. 
Temperature,  163. 
absolute,  168. 

Water,  expansion  of,  16*. 
latent  heat  of,  182. 
Water-level,  the,  97. 
Water-wheels,  1  13 
.  composition  of,  135. 
Weber,  the,.  34'- 

Thermal  balance,  the,  411. 
Thermo-electric  piles,  410. 
Thermometer,  air,  \i>-, 
alcohol,  1  66. 

Wedjie,  the,  67. 
Weight,  denned,  19. 
Wheatstone's  bridge,  345. 
Wheel  and  axle,  the,  62. 

differential,  if.  8. 

Wheels,  belted.  65. 

mercurial,  163. 

Wind  instruments,  144. 

Windlass,  the,  65. 

Thermopile,  the.  169. 
Thermophone,  the,  282. 
Thilorier's  liquefaction  of  carbonic  acid, 

Winds,  447- 
cause  of,  449- 
middle-latitude,  452. 

Thomson's  galvanometer,  337.  405. 
quadrant  electrometer,  312. 

polar,  453- 
systems  of,  451. 
trade,  451. 

tray  cell,  352- 
Thunder.  480. 

Work,  defined,  23. 
units  of,  24. 

Torricelli's  experiment,  104. 

Tr.insiiarent  bodies,  211. 

Y. 

Turbine  wheel,  the,  115. 
Twilight,  496- 

Young-Helmholtz  theory  of  color,  265. 

U- 

Z. 

Umbra  of  shadow,  2  1  1. 

Unison,  132 

Zero,  the  absolute,  168. 

SOUTH  E-rt 

UNIVERSITY  OF  CALIFOR 

LIBRARY, 

LOS  ANGELES,  CALIF 


